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Geometry : 

Geometry Chapter 8 Lesson 5

Slide 2: 

EXAMPLE 1 Use a coordinate plane SOLUTION Compare the slopes of opposite sides.

Slide 3: 

EXAMPLE 1 Use a coordinate plane

Slide 4: 

GUIDED PRACTICE for Example 1 1. What If? In Example 1, suppose the coordinates of point S are (4, 5). What type of quadrilateral is ORST? Explain. Compare the slopes of opposite sides. SOLUTION

Slide 5: 

GUIDED PRACTICE for Example 1

Slide 6: 

GUIDED PRACTICE for Example 1

Slide 7: 

EXAMPLE 2 Use properties of isosceles trapezoids SOLUTION

Slide 8: 

EXAMPLE 2 Use properties of isosceles trapezoids

Slide 9: 

EXAMPLE 3 Use the midsegment of a trapezoid Apply Theorem 8.17. Substitute 12 for PQ and 28 for XU. Simplify. = 20

Slide 10: 

GUIDED PRACTICE for Examples 2 and 3 In Exercises 3 and 4, use the diagram of trapezoid EFGH.

Slide 11: 

GUIDED PRACTICE for Examples 2 and 3

Slide 12: 

GUIDED PRACTICE for Examples 2 and 3

Slide 13: 

GUIDED PRACTICE for Examples 2 and 3 Apply Theorem 8.17. Substitute Simplify. Multiply each side by 2

Slide 14: 

EXAMPLE 4 Apply Theorem 8.19

Slide 15: 

Corollary to Theorem 8.1 Combine like terms. EXAMPLE 4 Apply Theorem 8.19

Slide 16: 

GUIDED PRACTICE for Example 4 6. In a kite, the measures of the angles are 3xo, 75o, 90o, and 120o. Find the value of x. What are the measures of the angles that are congruent? STEP 1 Sum of the angles in a quadrilateral = 360° Subtract Divided by 3 from each side Combine like terms SOLUTION

Slide 17: 

GUIDED PRACTICE for Example 4 STEP 2 = 75 Substitute Simplify