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ELED 4315 - Alief Cluster Fall 2005 lex D. Jones ngela Patterson iffany King amika Ewing.

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Presentation on theme: "ELED 4315 - Alief Cluster Fall 2005 lex D. Jones ngela Patterson iffany King amika Ewing."— Presentation transcript:

1 ELED Alief Cluster Fall 2005 lex D. Jones ngela Patterson iffany King amika Ewing

2 Pyramid – natural T extbook E xample This is a picture from the internet of a rock shaped in the form of a pyramid. A pyramid is a geometric shape formed by connecting a polygonal base and a point, called the apex, by triangular faces. This is a picture from the internet of a rock shaped in the form of a pyramid. A pyramid is a geometric shape formed by connecting a polygonal base and a point, called the apex, by triangular faces.

3 Pyramid – man made T extbook E xample This is a picture from the internet of the convention center in Memphis, TN. A pyramid is a geometric shape formed by connecting a polygonal base and a point, called the apex, by triangular faces. This is a picture from the internet of the convention center in Memphis, TN. A pyramid is a geometric shape formed by connecting a polygonal base and a point, called the apex, by triangular faces.

4 Arc - natural T extbook E xample This is a picture of a Rainbow over the river Teifi. A rainbow is an arc of concentric colored bands that develops when sunlight interacts with rain dropsRainbow over the river Teifi An arc is a curved line that is part of a circle.. This is a picture of a Rainbow over the river Teifi. A rainbow is an arc of concentric colored bands that develops when sunlight interacts with rain dropsRainbow over the river Teifi An arc is a curved line that is part of a circle..

5 Arc – man made T extbook E xample This is a picture of the Arc du Triumph which is an example of a man made arc. An arc is a curved line that is part of a circle. This is a picture of the Arc du Triumph which is an example of a man made arc. An arc is a curved line that is part of a circle.

6 Cone - natural T extbook E xample This is a picture of a carrot taken from the internet. A cone is a solid object obtained by rotating a right triangle around one of its two short sides, the cone's axis. This is a picture of a carrot taken from the internet. A cone is a solid object obtained by rotating a right triangle around one of its two short sides, the cone's axis.

7 Cone – man made T extbook E xample This is a picture of a traffic cone taken at Outley Elementary. A cone is a solid object obtained by rotating a right triangle around one of its two short sides, the cone's axis. This is a picture of a traffic cone taken at Outley Elementary. A cone is a solid object obtained by rotating a right triangle around one of its two short sides, the cone's axis.

8 Square – natural T extbook E xample This is a picture of a rock in the fountain at the University of Houston. A square is a plane rectangle with four equal sides and four right angles. Although not a perfect square this picture typifies a square because it contains four equal sides and four right angles. This is a picture of a rock in the fountain at the University of Houston. A square is a plane rectangle with four equal sides and four right angles. Although not a perfect square this picture typifies a square because it contains four equal sides and four right angles.

9 Square – man made T extbook E xample This is a picture of a rug in Alexs apartment, the square rug is made up of smaller squares. This picture typifies a square because it contains four equal sides and four right angles. A square is a plane rectangle with four equal sides and four right angles. This is a picture of a rug in Alexs apartment, the square rug is made up of smaller squares. This picture typifies a square because it contains four equal sides and four right angles. A square is a plane rectangle with four equal sides and four right angles.

10 Pentagon– natural T extbook E xample This is a picture of a starfish taken from the internet, the points of the starfish creates five angles and sides. A pentagon is a polygon having five angles and five sides. This is a picture of a starfish taken from the internet, the points of the starfish creates five angles and sides. A pentagon is a polygon having five angles and five sides.

11 Pentagon– man made T extbook E xample A B C D E This is a picture of a tent taken from the internet, this picture typifies a pentagon because each side of the tent has five angles. A pentagon is a polygon having five angles and five sides. This is a picture of a tent taken from the internet, this picture typifies a pentagon because each side of the tent has five angles. A pentagon is a polygon having five angles and five sides.

12 Ellipse– natural T extbook E xample This is an example of planet moving around a sun. The rotation of a planet around the sun or a moon around a planet can be an ellipse because of the pattern of rotation around the center. An ellipse is a geometric figure resembling an elongated circle. An ellipse is characterized by its degree of flatness, and the length of its long axis. This is an example of planet moving around a sun. The rotation of a planet around the sun or a moon around a planet can be an ellipse because of the pattern of rotation around the center. An ellipse is a geometric figure resembling an elongated circle. An ellipse is characterized by its degree of flatness, and the length of its long axis.

13 Ellipse– man made T extbook E xample This is a race track and an amusement park ride called the Zipper. Both a race car track and an amusement park ride can be an ellipse because the cars travel on an oblong course around a central point as do the cages on a ride. An ellipse is a geometric figure resembling an elongated circle. An ellipse is characterized by its degree of flatness, and the length of its long axis. This is a race track and an amusement park ride called the Zipper. Both a race car track and an amusement park ride can be an ellipse because the cars travel on an oblong course around a central point as do the cages on a ride. An ellipse is a geometric figure resembling an elongated circle. An ellipse is characterized by its degree of flatness, and the length of its long axis.

14 Prism– natural T extbook E xample This is a quartz crystal. A crystal is a prism because it joins two congruent polygonal regions on parallel planes. The solid figure formed by joining two congruent polygonal regions in parallel planes is called a prism. The polygonal regions are called bases and the other surfaces are lateral faces. This is a quartz crystal. A crystal is a prism because it joins two congruent polygonal regions on parallel planes. The solid figure formed by joining two congruent polygonal regions in parallel planes is called a prism. The polygonal regions are called bases and the other surfaces are lateral faces.

15 Prism– man made T extbook E xample This is a man made prism. This man made prism qualifies because it has three sides that have polygonal parallel surfaces that are joined together. This is a man made prism. This man made prism qualifies because it has three sides that have polygonal parallel surfaces that are joined together.

16 Parabola– natural T extbook E xample This is a sand dune. These sand dunes for parabolas because of the curve that is created. A parabola is a plane curve formed by the intersection of a right circular cone and a plane parallel to an element of the cone or by the focus of points equidistant from a fixed line and a fixed point not on the line. This is a sand dune. These sand dunes for parabolas because of the curve that is created. A parabola is a plane curve formed by the intersection of a right circular cone and a plane parallel to an element of the cone or by the focus of points equidistant from a fixed line and a fixed point not on the line.

17 Parabola– man made T extbook E xample This is a type of suspension bridge. The curve of the suspension bearing beams of this bridge form a parabola because of the curve that it creates. A parabola is a plane curve formed by the intersection of a right circular cone and a plane parallel to an element of the cone or by the focus of points equidistant from a fixed line and a fixed point not on the line. This is a type of suspension bridge. The curve of the suspension bearing beams of this bridge form a parabola because of the curve that it creates. A parabola is a plane curve formed by the intersection of a right circular cone and a plane parallel to an element of the cone or by the focus of points equidistant from a fixed line and a fixed point not on the line.

18 Line – natural T extbook E xample This is a picture of the ocean surrounding an island. The ocean forms a line of horizon. The horizon extends in opposite directions and does not end. A line can be thought of as a set of points in a one-dimensional straight figure that extends in opposite directions without ending. This is a picture of the ocean surrounding an island. The ocean forms a line of horizon. The horizon extends in opposite directions and does not end. A line can be thought of as a set of points in a one-dimensional straight figure that extends in opposite directions without ending.

19 Line – man made T extbook E xample This is a path between rows of crops. This is a man made line, although the line does eventually end it is not seen here. A line can be thought of as a set of point in a one-dimensional straight figure that extends in opposite directions without ending. This is a path between rows of crops. This is a man made line, although the line does eventually end it is not seen here. A line can be thought of as a set of point in a one-dimensional straight figure that extends in opposite directions without ending.

20 Transversal – natural T extbook E xample This is an image of died cells. This slide of cells demonstrates transversal because the vertical line of cells intersects at two distinct points with horizontal lines in the slide. A transversal is a line that intersects two or more distinct lines in different points. This is an image of died cells. This slide of cells demonstrates transversal because the vertical line of cells intersects at two distinct points with horizontal lines in the slide. A transversal is a line that intersects two or more distinct lines in different points.

21 Transversal – man made T extbook E xample The books shelves are transversal because the horizontal shelf in the center of the unit intersect at two distinct points with vertical supports. A transversal is a line that intersects two or more distinct lines in different points. The books shelves are transversal because the horizontal shelf in the center of the unit intersect at two distinct points with vertical supports. A transversal is a line that intersects two or more distinct lines in different points.

22 Quadrilateral – natural T extbook E xample This is a spider web in a door frame. This spider web has many examples of quadrilaterals as the silk that forms the web connects with itself at four points. A quadrilateral is a closed figure in a plane. It has four segments called sides that intersect only at their endpoints. Each endpoint is called the vertex of the quadrilateral. No two consecutive sides are on the same line. This is a spider web in a door frame. This spider web has many examples of quadrilaterals as the silk that forms the web connects with itself at four points. A quadrilateral is a closed figure in a plane. It has four segments called sides that intersect only at their endpoints. Each endpoint is called the vertex of the quadrilateral. No two consecutive sides are on the same line.

23 Quadrilateral – man made T extbook E xample This sign is a quadrilateral because it has four sides that connect with each other on the same plane. A quadrilateral is a closed figure in a plane. It has four segments called sides that intersect only at their endpoints. Each endpoint is called the vertex of the quadrilateral. No two consecutive sides are on the same line. This sign is a quadrilateral because it has four sides that connect with each other on the same plane. A quadrilateral is a closed figure in a plane. It has four segments called sides that intersect only at their endpoints. Each endpoint is called the vertex of the quadrilateral. No two consecutive sides are on the same line.

24 Similar Items – natural T extbook E xample These two armadillos are the same shape even though they are in different positions. One is a baby an one is an adult. Figures that have the same shape are called similar figures. They may be different sizes or turned somewhat.. These two armadillos are the same shape even though they are in different positions. One is a baby an one is an adult. Figures that have the same shape are called similar figures. They may be different sizes or turned somewhat..

25 Similar Items – man made T extbook E xample These two Fords are the exact same model even they are turned differently they have the same shape. One is the normal size of a car and the other is a 1:64 model. Figures that have the same shape are called similar figures. They may be different sizes or turned somewhat.. These two Fords are the exact same model even they are turned differently they have the same shape. One is the normal size of a car and the other is a 1:64 model. Figures that have the same shape are called similar figures. They may be different sizes or turned somewhat..

26 Cylinder – natural T extbook E xample These are very tall trees in a forest. Although not a perfect cylinders from top to bottom these trees do form cylinders at certain given segments because the wood connects two circles in parallel planes. The solid figure formed by joining two congruent circles in parallel planes is called a cylinder. These are very tall trees in a forest. Although not a perfect cylinders from top to bottom these trees do form cylinders at certain given segments because the wood connects two circles in parallel planes. The solid figure formed by joining two congruent circles in parallel planes is called a cylinder.

27 Cylinder – man made T extbook E xample This is a can of Pillsbury buttermilk biscuits. This can of biscuits is a cylinder because it forms a solid figure when the paper wrapping joins the to metal end pieces that are circles. The solid figure formed by joining two congruent circles in parallel planes is called a cylinder. This is a can of Pillsbury buttermilk biscuits. This can of biscuits is a cylinder because it forms a solid figure when the paper wrapping joins the to metal end pieces that are circles. The solid figure formed by joining two congruent circles in parallel planes is called a cylinder.

28 Sphere – natural T extbook E xample This is a pearl. It is a sphere because the surface is the same distance from the center at any given point. A sphere is the set of all points in space at a given distance, called the radius, from a given point, called the center. This is a pearl. It is a sphere because the surface is the same distance from the center at any given point. A sphere is the set of all points in space at a given distance, called the radius, from a given point, called the center.

29 Sphere – man made T extbook E xample This is a sphere that marks the true south pole. It is the same distance to the surface from the center all of the way around. A sphere is the set of all points in space a given distance, called the radius, from a given point, called the center. This is a sphere that marks the true south pole. It is the same distance to the surface from the center all of the way around. A sphere is the set of all points in space a given distance, called the radius, from a given point, called the center.

30 Intersecting Lines – natural T extbook E xample These tree branches cross each other at the same point in several place at the same point. Intersecting lines are two lines that meet at a point. These tree branches cross each other at the same point in several place at the same point. Intersecting lines are two lines that meet at a point.

31 Intersecting Lines – man made T extbook E xample Interior of a home composed of a system of intersecting lines. Intersecting lines are two lines that meet at a point. Interior of a home composed of a system of intersecting lines. Intersecting lines are two lines that meet at a point.

32 Angle – natural T extbook E xample This lily leaf is an example of an angle. Two rays that share the same endpoint form an angle. The point where the rays intersect is called the vertex of the angle. The two rays are called the sides of the angle. This lily leaf is an example of an angle. Two rays that share the same endpoint form an angle. The point where the rays intersect is called the vertex of the angle. The two rays are called the sides of the angle.

33 Angle – man made T extbook E xample Angles are formed on this windmill because each part shares the same middle point which can be seen at the middle of the windmill. Two rays that share the same endpoint form an angle. The point where the rays intersect is called the vertex of the angle. The two rays are called the sides of the angle. Angles are formed on this windmill because each part shares the same middle point which can be seen at the middle of the windmill. Two rays that share the same endpoint form an angle. The point where the rays intersect is called the vertex of the angle. The two rays are called the sides of the angle.

34 Circle – natural T extbook E xample A red circle can be seen on the inside of this flower. The red area is equal distance from the center of the flower. A circle is the set of all points in a plane at a fixed distance, called the radius, and from a fixed point, called the center. A red circle can be seen on the inside of this flower. The red area is equal distance from the center of the flower. A circle is the set of all points in a plane at a fixed distance, called the radius, and from a fixed point, called the center.

35 Circle – man made T extbook E xample This basketball is considered to be a circle because the outer layer is equal distance from the center. A circle is the set of all points in a plane at a fixed distance, called the radius, from a fixed point, called the center. This basketball is considered to be a circle because the outer layer is equal distance from the center. A circle is the set of all points in a plane at a fixed distance, called the radius, from a fixed point, called the center.

36 Chord – natural T extbook E xample The suns two endpoints is a good example of a chord because it is being cut by the water. A chord is a line segment within a circle that touches 2 points on the circle. The suns two endpoints is a good example of a chord because it is being cut by the water. A chord is a line segment within a circle that touches 2 points on the circle.

37 Chord – man made T extbook E xample The ice cream displays a cord because the rounded ice cream has been cut at the two sides by the cone. A chord is a line segment within a circle that touches 2 points on the circle. The ice cream displays a cord because the rounded ice cream has been cut at the two sides by the cone. A chord is a line segment within a circle that touches 2 points on the circle.

38 Plane – natural T extbook E xample These flowers are floating on top of of the water which is the plane because it spreads infinite directions. A plane is a two-dimensional group of points that goes on infinitely in all directions; made up of infinite lines. These flowers are floating on top of of the water which is the plane because it spreads infinite directions. A plane is a two-dimensional group of points that goes on infinitely in all directions; made up of infinite lines.

39 Plane – man made T extbook E xample A football field is a good example of a plane because the points and lines on the plane are infinite. A plane is a two-dimensional group of points that goes on infinitely in all directions; made up of infinite lines. A football field is a good example of a plane because the points and lines on the plane are infinite. A plane is a two-dimensional group of points that goes on infinitely in all directions; made up of infinite lines.

40 Triangle – natural T extbook E xample This spider web displays several triangles by the lines from the center extending outward that make the two long sides. The bottoms of the triangles are formed by the lines that intersect the longer sides. A triangle is a three-sided polygon. This spider web displays several triangles by the lines from the center extending outward that make the two long sides. The bottoms of the triangles are formed by the lines that intersect the longer sides. A triangle is a three-sided polygon.

41 Triangle – man made T extbook E xample This ladder display two triangles with the two long sides of wood and the floor making the third side. A triangle is a three-sided polygon. This ladder display two triangles with the two long sides of wood and the floor making the third side. A triangle is a three-sided polygon.

42 Tangent – natural T extbook E xample The tangent can be seen in this picture by the circle, the snowball, touching the line, the hill, at a given point. A tangent is a straight line or plane that touches a curve or curved surface at a point but does not intersect it at that point. The tangent can be seen in this picture by the circle, the snowball, touching the line, the hill, at a given point. A tangent is a straight line or plane that touches a curve or curved surface at a point but does not intersect it at that point.

43 Tangent – man made T extbook E xample The tangent can be seen in this picture by the circle, the snowball, touching the line, the hill, at a given point. A tangent is a straight line or plane that touches a curve or curved surface at a point but does not intersect it at that point. The tangent can be seen in this picture by the circle, the snowball, touching the line, the hill, at a given point. A tangent is a straight line or plane that touches a curve or curved surface at a point but does not intersect it at that point.

44 Cube – natural T extbook E xample These rocks have been stacked on top of each to display only one face but there are six faces total. A cube is a regular solid body, with six equal square sides.square These rocks have been stacked on top of each to display only one face but there are six faces total. A cube is a regular solid body, with six equal square sides.square

45 Cube – man made T extbook E xample This toy has 6 faces, all of which are equal. A cube is a regular solid body, with six equal square sides.square This toy has 6 faces, all of which are equal. A cube is a regular solid body, with six equal square sides.square

46 Parallel Lines cut by a non-perpendicular transversal – natural T extbook E xample The facets of this crystal form parallel lines that are cut by a non-perpendicular transversal at the tip. A transversal is a line that intersects a system of other lines. It is non-perpendicular when it has any slope other than -1. This creates acute and obtuse angles. transversal The facets of this crystal form parallel lines that are cut by a non-perpendicular transversal at the tip. A transversal is a line that intersects a system of other lines. It is non-perpendicular when it has any slope other than -1. This creates acute and obtuse angles. transversal

47 Parallel Lines cut by a non-perpendicular transversal – man made T extbook E xample The support lumber create non-perpendicular transversals to the parallel lines created by the other parts of the wood. A transversal is a line that intersects a system of other lines. It is non-perpendicular when it has any slope other than -1. This creates acute and obtuse angles. transversal The support lumber create non-perpendicular transversals to the parallel lines created by the other parts of the wood. A transversal is a line that intersects a system of other lines. It is non-perpendicular when it has any slope other than -1. This creates acute and obtuse angles. transversal

48 Point – natural T extbook E xample The tree branches have points on opposite ends of each other. A point has no length or width, it just specifies a location. The tree branches have points on opposite ends of each other. A point has no length or width, it just specifies a location.

49 Point – man made T extbook E xample The safety pin has a sharp point at the end of it. A point has no length or width, it just specifies a location. The safety pin has a sharp point at the end of it. A point has no length or width, it just specifies a location.

50 Parallel lines – natural T extbook E xample These parallel lines are found in space. Two lines in the same plane which never intersect are called parallel lines. These parallel lines are found in space. Two lines in the same plane which never intersect are called parallel lines.

51 Parallel lines – natural T extbook E xample These are man-made parallel lines find on an outside deck. Two lines in the same plane which never intersect are called parallel lines. These are man-made parallel lines find on an outside deck. Two lines in the same plane which never intersect are called parallel lines.

52 Pythagorean triple – natural T extbook E xample The tree represents a Pythagorean triple because it has the parts a, b, and c. A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2, which forms a right triangle.integers The tree represents a Pythagorean triple because it has the parts a, b, and c. A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2, which forms a right triangle.integers

53 Pythagorean triple – man made T extbook E xample This image of the right triangle represents the Pythagorean triple. This image was found on a walkway to a shopping center. A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2, which forms a right triangle.integers This image of the right triangle represents the Pythagorean triple. This image was found on a walkway to a shopping center. A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2, which forms a right triangle.integers

54 Fractal – natural T extbook E xample Romanesco broccoli showing very fine natural fractals. A fractal is a geometric object which is irregular or rough on all scales of length, and so it appears to be broken up. Romanesco broccoli showing very fine natural fractals. A fractal is a geometric object which is irregular or rough on all scales of length, and so it appears to be broken up.

55 Fractal – man made T extbook E xample This is a computer generated fractal from Sprott's Fractal Gallery. Sprott's Fractal Gallery A fractal is a geometric object which is irregular or rough on all scales of length, and so it appears to be broken up. This is a computer generated fractal from Sprott's Fractal Gallery. Sprott's Fractal Gallery A fractal is a geometric object which is irregular or rough on all scales of length, and so it appears to be broken up.

56 Oval – natural T extbook E xample This image of water bug can be found out doors in the spring and summer. An oval is a curved shaped somewhat like an egg or a speed racing track. This image of water bug can be found out doors in the spring and summer. An oval is a curved shaped somewhat like an egg or a speed racing track.

57 Oval – man made T extbook E xample This blue sapphire oval can be found in any piece of fine jewelry. An oval is a curved shaped somewhat like an egg or a speed racing track. This blue sapphire oval can be found in any piece of fine jewelry. An oval is a curved shaped somewhat like an egg or a speed racing track.

58 Congruent Items – natural T extbook E xample The leaf was found on the web to depict congruency of all sides. Congruent items are angles or figures that have the same size and shape. The leaf was found on the web to depict congruency of all sides. Congruent items are angles or figures that have the same size and shape.

59 Congruent Items – man made T extbook E xample This figure is congruent on all sides and can be found on the web. Two polygons are congruent if they are the same size and shape. This figure is congruent on all sides and can be found on the web. Two polygons are congruent if they are the same size and shape.

60 Ray – natural T extbook E xample The rays in the sky were found on the internet A ray is a "straight" line that begins at a certain point and extends forever in one direction. The point where the ray begins is known as its endpoint. The rays in the sky were found on the internet A ray is a "straight" line that begins at a certain point and extends forever in one direction. The point where the ray begins is known as its endpoint.

61 Ray – man made T extbook E xample This is a ray of light from a laser beam. A ray is a "straight" line that begins at a certain point and extends forever in one direction. The point where the ray begins is known as its endpoint. This is a ray of light from a laser beam. A ray is a "straight" line that begins at a certain point and extends forever in one direction. The point where the ray begins is known as its endpoint.

62 Parallel Lines cut by a transversal – natural T extbook E xample The stems of the plant are cut by the stream of the water which is the transversal. Two lines are parallel if they never meet. A line that intersects two parallel lines is a transversal. The stems of the plant are cut by the stream of the water which is the transversal. Two lines are parallel if they never meet. A line that intersects two parallel lines is a transversal.

63 Parallel Lines cut by a transversal – man made T extbook E xample This image found on the internet is of two fence boards parallel to another fence boards that cut straight through it. Two lines are parallel if they never meet. A line that intersects two parallel lines is a transversal. This image found on the internet is of two fence boards parallel to another fence boards that cut straight through it. Two lines are parallel if they never meet. A line that intersects two parallel lines is a transversal.

64 RESOURCES Introduction to Geometry Glossary of Geometric and Mathematical Terms Introduction to Geometry Glossary of Geometric and Mathematical Terms


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