 # GEOMETRY.

## Presentation on theme: "GEOMETRY."— Presentation transcript:

GEOMETRY

PLANE FIGURES A plane is a flat surface that goes on and on in all directions. A plane figure is a flat geometric shape. POLYGONS A polygon is a closed plane figure made up of three or more line segments (sides) that are connected.

vertices A vertex is the point where two sides of a polygon meet.
The plural of vertex is vertices. vertices

Polygons are named by the number of sides they have.
A triangle has 3 sides. A quadrilateral has 4 sides. A pentagon has 5 sides. There are also names for polygons with seven sides, nine sides, and any number of sides! A hexagon has 6 sides. An octagon has 8 sides.

PERIMETER The perimeter of a figure is the distance around the outside. What is the perimeter of each of these polygons? 12 in. 8 units 6 in. 6 in. 9 units 9 units P = 36 in. P = 37 units 11 units 12 in. 15 m. 5 m. P = 39 m. 16 ft. 16 ft. 5 m. 4 m. P = 50 ft. 10 m. 18 ft.

AREA The area of a flat surface is the number of square units needed to cover the surface. What is the area of each of these polygons? Count the square units to find out. A = 20 sq. units A = 104 sq. units

AREA The area of a flat surface is the number of square units needed to cover the surface. What is the area of each of these rectangles? Multiply to find out. 4 units 4 units A = 8 x 13 = 104 sq. units A = 4 x 4 = 16 sq. units

CIRCLES A circle is a closed curve that is made of points that are the same distance from the center. A line segment is a part of a line. A radius is any line segment that connects the center to a point on the circle. A diameter is any line segment that passes through the center of a circle, connecting two points on the circle. A diameter is twice as long as a radius.

CIRCLES The circumference is the distance around a circle. The circumference of a circle is about 3 times the diameter. C = about 3 x d

CIRCLES The area of a circle is the number of square units needed to cover the inside of the circle. Find the approximate area of a circle by counting the square units inside or by multiplying the radius times the radius times 3. A = about 3 x r x r

CIRCLES P = about ______ units. A = about ______ sq. units. 18 36 27
Find the approximate perimeters of the circles below. R = 3 units R = 6 units P = about ______ units. A = about ______ sq. units. 18 36 27 P = about ______ units. A = about ______ sq. units. 108

CONGRUENT FIGURES Congruent figures have the same size and shape.

SIMILAR FIGURES Similar figures have the same shape. If they also have the same size, they are congruent.

MOVING PLANE FIGURES A slide (translation) moves a figure up, down, or over.

MOVING PLANE FIGURES A turn (rotation) rotates a plane figure.

MOVING PLANE FIGURES A flip (reflection) is a mirror image of a figure.

SYMMETRY A plane figure has symmetry if its halves match.
If a plane figure has symmetry, it can be folded so its halves match. The fold is called a line of symmetry.

SYMMETRY How many lines of symmetry do each of these plane figures have?

TESSELLATIONS (TILING)
A tessellation completely covers the inside space of a plane figure, usually in some kind of organized pattern.

Now use the tiles to experiment
Now use the tiles to experiment. Which tiles will tessellate a piece of math paper? Try squares, triangles, hexagons, etc. Will circles tessellate a plane figure? Explain your answer.

SOLID GEOMETRY A three-dimensional object is called a space figure or a solid. cube cylinder rectangular prism pyramid sphere cone

SOLID GEOMETRY VOCABULARY
FACE pyramid rectangular prism cube sphere cylinder cone

SOLID GEOMETRY VOCABULARY
VERTEX pyramid rectangular prism cube sphere cylinder cone

SOLID GEOMETRY VOCABULARY
EDGE pyramid rectangular prism cube sphere cylinder cone

= one cubic unit 6 V = ______ cubic units
The number of cubic units inside a solid is called the volume. 6 V = ______ cubic units

= one cubic unit 24 V = ______ cubic units
The number of cubic units inside a solid is called the volume. 24 V = ______ cubic units

Count the cubic units to find the volume of this figure.
SOLID GEOMETRY Count the cubic units to find the volume of this figure. V = ______ cubic units 22

V = ______ cubic units 36

GEOMETRY VOCABULARY TERM EXAMPLE SAY A
A point is an exact location in space. A point A A line is a collection of points that go on and on in both directions. It has no endpoints. C line BC A line segment is part of a line. It has two endpoints. line segment DE A ray is part of a line. It has one endpoint and continues on and on in one direction. F G ray FG Intersecting lines are lines that pass through the same point. line HK intersects line JI at point L Parallel lines are lines that never intersect. line JK is parallel to line BC. B BB D E H L I J K J K J K B C

GEOMETRY VOCABULARY Two intersecting lines that form four right angles are perpendicular to each other. A C B D Line BC is perpendicular to line AD.

GEOMETRY VOCABULARY Two rays meet at a vertex, forming an angle.
An angle that forms a square corner is a right angle. An angle greater than a right angle is an obtuse angle. An angle less than a right angle is an acute angle.