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Geometry

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Points, Rays, and Lines This is a point. A point represents one place in space. This is a ray. A ray is a straight line of points that begins at one point and goes in one direction. This is a line. A line is a straight path of points that goes in two directions. This is a line segment. A line segment is a straight line that begins and ends on two points. Go On

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More Lines These lines are parallel. They run in the same direction and never cross. These lines are perpendicular. They cross at right angles. This is a horizontal line. This is a vertical line. This is the point of intersection. Go On

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Matching Match the symbol on the left with its name on the right. Horizontal line Line segment Point ray Vertical line Perpendicular lines Parallel lines Line Go On

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Angles This is an angle. It is formed by two rays extending from the same point. This is the vertex. It is where the two rays in an angle begin. This is an acute angle. It measures less than. This is a right angle. It measures exactly. This is an obtuse angle. It measures more than but less than. This is a straight angle. It measures exactly. This is a reflex angle. It measures greater than. A degree is a unit which angles are measured. Go On

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Matching Match the angle on the left with its name on the right. Reflex angle Right angle Vertex Straight angle Acute angle Obtuse angle Go On

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Angles are Everywhere Acute angle Right angle Obtuse angle Go On

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More Lines and Angles acute obtuse acute obtuse reflex right Perpendicular lines Parallel lines Go On

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Lines and Angles in Real Life Match the words in the center with their examples on the left or right sides. Perpendicular lines Parallel lines Reflex angle Obtuse angle Right angle Acute angle Go On

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Angle Relationships This symbol represents an angle. An angle’s name has the vertex as its center. This angle’s name is ABC. A B C D E F G W X Y Z Supplementary Angles Supplementary Angles are two angles that add up to 180°. For example, in the figure below, DEF + FEG = 180°. Complementary Angles Complementary Angles are two angles that add up to 90°. For example, in the figure below, WXY + YXZ = 90°. Go On

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HI J KL O P Q RS T U V Transversal Line A Transversal line is a line that crosses parallel lines. In the figure below, the line with points TSPQ is a transversal line. Congruent Congruent means equal. When a transversal line cuts through two parallel lines, the alternate interior and alternate exterior angles that are formed are congruent. The following angles are congruent: OPQ RSP QPV PSU TSU SPV RST OPS SPV TSU Adjacent Angles Adjacent angles are two angles that share a side. For example, in the figure below, HIJ and JIL and HIK and KIL are adjacent angles. Vertical Angles The angles that are across from each other (opposite) when two lines intersect each other are called Vertical Angles. Vertical angles (opposite angles) are equal. The following angles are vertical angles: HIK JIL HIJ KIL Go On

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Measuring Complementary and Supplementary Angles When you are using both complementary and supplementary angles, it is important to remember that if you know the measurement of one of the angles, you can find the measurement of the other angle. Remember that Complementary Angles are two angles which add up to 90º. Supplementary angles are two angles which add up to 180º. A B C D 30° Y WXZ 65° 60° 115° Click Here for a Problem Click Here for Answer Go On

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Basic Geometric Shapes SquareA Square is made up of 4 right angles (90° angles) and has 4 sides which are equal in length. Rectangle A rectangle is a shape that is made up of 4 right angles. The sides opposite each other are parallel and equal in length. parallel Go On

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More Shapes Triangle A Triangle is a shape that has three sides. The 3 angles that make up a triangle equal 180°. CircleA Circle is a shape in which all points that make up the circle are exactly the same distance from the center of the circle. The distance across the center of the circle, which cuts the circle in 2 equal parts, is called the diameter. The distance from the center of the circle to a point on the outside of the circle is the radius. Right TriangleA Right Triangle is a shape that has 3 sides. One angle (a right angle) is 90°; the right angle plus the other 2 angles equals 180°. The side opposite the right angle is called the hypotenuse. The other 2 sides are called legs. radius diameter Legs hypotenuse Go On

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Shapes Are All Around Us Square Triangle Rectangle Right Triangle Circles Go On

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The Pythagorean Theorem a b c The Pythagorean Theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. The formula for finding the length of the sides of any right triangle is as follows: Geometry is used in many different occupations by carpenters, architects, graphic artists, and engineers, just to name a few. It is used in designs, construction, and drawings. Many of these workers need to know the Pythagorean Theorem. Go On

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Using the Pythagorean Theorem 3 4 c Go On

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Test Yourself 1.What shape is a floor tile that measures 6 inches by 6 inches? RectangleTriangleCircle Square 2. If your bedroom measures 15 feet wide and 10 feet long, what is the shape of your bedroom? SquareTriangleCircle Rectangle 3. A pizza has a diameter of 12 inches. What shape is your pizza? SquareRectangleTriangle Circle SquaresRectanglesCircles 4. What shape are these objects? Triangles Go On 5. A Right Triangle has legs 5 and 12 inches long. How long is the hypotenuse? 17 inches34 inches25 inches 13 inches

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Polygons Polygons are closed figures (all the segments meet) with three or more sides. OctagonHexagon Pentagon Triangle Rectangle Rhombus Trapezoid Diamond Square Shapes with four sides and only four sides are called quadrilaterals. A Rectangle, Rhombus, Parallelogram, Trapezoid, Diamond, and Square are all quadrilaterals. A Rhombus is also called a Parallelogram. Go On

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Click on the correct answer. A Quadrilateral shape has ______ sides.OneFiveThree Four The sides of a Square areDifferent LongDiagonal Equal A shape with three sides is called aSquare Rhombus Circle Triangle How many sides are in a pentagon?OneTwoThree Five Which of these is not a parallelogram?Rectangle Square Rhombus Hexagon Which of these is not a quadrilateral?Rectangle Square Rhombus Triangle A parallelogram has opposite sides that are EqualShortLong Parallel The distance across the center of a circle is called the RadiusLengthWidth Diameter Go On

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Perimeter and Area of Polygons Perimeter is the distance around the outside of a shape. For example, to find the Perimeter of a Rectangle below, add the lengths of all four sides together The Perimeter of the Rectangle is 30. Area is the measure of the space within the perimeter of a shape. To find the Area of the Rectangle below, multiply one length by one width The Area of the Rectangle is 50. Go On

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Area and Perimeter of Triangles Just like other polygons, to compute the perimeter of a Triangle, you add the sides together To compute the area of a Triangle, you multiply The Perimeter of this triangle is The Area of this triangle is 35. Go On

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Circles The distance around the outside of a circle is called the Circumference. To find the circumference of a circle, you use a symbol called pi ( ). The formula for the circumference of a circle is diameter. The value of The circumference of this circle is To find the area of a circle, use this formula: (r = radius). Remember, the radius of a circle is half of its diameter diameter radius Go On

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Practice – Find the Perimeter or Circumference of each shape Click for the Problem Click for the Solution Go On

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Find the Area of each Shape Click for the Problem Click for the Solution Go On

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Three-Dimensional Solids Cube Cylinder Rectangular Solid Cone Sphere Go On

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Three-Dimensional Solids Cone CubeSphere Cylinder Rectangular Solid Go On

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Cube For a cube or rectangular solid, use the formula For a cylinder, use this formula: Volume is the measure of space inside a three-dimensional (not flat) figure. Volume Go On Rectangular Solid Cylinder

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Volume Formulas To find the volume of a cone, use this formula: To find the volume of a sphere, use this formula: Go On Sphere Cone

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Practice Click the correct answer. A soccer cone is 8 inches high, with a radius of 5 inches. What is its volume? 8 5 A box is 10 inches long by 5 inches wide by 7 inches tall. What is its volume? Go On

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Practice A pair of fuzzy dice have sides which are 4 inches each. What is the volume of one die? What is the volume of a can of soup that has a radius of 10 cm and a height of 20 cm? Go On

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Review Horizontal Line Vertical Line Parallel Lines Perpendicular Lines Line segment Ray Acute Angle Right Angle Obtuse Angle Straight Angle Reflex Angle Go On

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Review Supplementary Angles add up to 180° Complementary Angles add up to 90° Adjacent Angles are two angles that share a side. A Transversal Line is a line that crosses parallel lines. Vertical Angles (Opposite Angles) are Congruent. Congruent means equal. Go On

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Review radius diameter Legs hypotenuse OctagonHexagon Right Triangle Rectangle Rhombus Trapezoid Diamond Square Circle A Quadrilateral Polygon has four sides. A Polygon is a figure with three or more sides.Pentagon Triangle Go On (A Circle is not a polygon.) The Pythagorean Theorem is

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Review To find the Area of a Polygon, multiply its length by its width. To find the Area of a Circle, use this formula: where r is the radius. To find the Area of a Triangle, multiply its height by half of its base: To find the Perimeter of a Polygon, add all of its sides together. To find the Circumference of a Circle, multiply the diameter by (3.14). Diameter Radius h b Go On Use this formula to find the Volume of a Cube or Rectangular Solid: Use this formula to find the Volume of a Cylinder: Use this formula to find the Volume of a Cone: Use this formula to find the Volume of a Sphere:

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Keep Practicing!

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