1. Lesson 8-6 Trapezoids Theorem 8.18
Both pairs of base angles of an isosceles trapezoid are congruent
Theorem 8.19
The diagonals of an isosceles trapezoid are congruent.
Theorem 8.20
The median of a trapezoid is parallel to the bases and its measure is one-half the sum of the measures of the bases.

2. Given: KLMN is an isosceles trapezoid.
Write a flow proof.
Given: KLMN is an isosceles trapezoid.
Prove:
Example 6-1a

3. Proof:
Example 6-1a

4. Given: ABCD is an isosceles trapezoid.
Write a flow proof.
Given: ABCD is an isosceles trapezoid.
Prove:
Example 6-1b

5. Proof:
Example 6-1b

6. Answer: Both trapezoids are isosceles.
The top of this work station appears to be two adjacent trapezoids. Determine if they are isosceles trapezoids.
Each pair of base angles is congruent, so the legs are the same length.
Answer: Both trapezoids are isosceles.
Example 6-2a

7. The sides of a picture frame appear to be two adjacent trapezoids
The sides of a picture frame appear to be two adjacent trapezoids. Determine if they are isosceles trapezoids.
Answer: yes
Example 6-2b

8. ABCD is a quadrilateral with vertices A(5, 1), B(–3, –1), C(–2, 3), and D(2, 4). Verify that ABCD is a trapezoid.
A quadrilateral is a trapezoid if exactly one pair of opposite sides are parallel. Use the Slope Formula.
Example 6-3a

9. slope of slope of slope of slope of
Answer: Exactly one pair of opposite sides are parallel, So, ABCD is a trapezoid.
Example 6-3b

10. ABCD is a quadrilateral with vertices A(5, 1), B(–3, 1), C(–2, 3), and D(2, 4). Determine whether ABCD is an isosceles trapezoid. Explain.
Example 6-3c

11. First use the Distance Formula to show that the legs are congruent.
Answer: Since the legs are not congruent, ABCD is not an isosceles trapezoid.
Example 6-3d

12. a. Verify that QRST is a trapezoid.
QRST is a quadrilateral with vertices Q(–3, –2), R(–2, 2), S(1, 4), and T(6, 4).
a. Verify that QRST is a trapezoid.
Answer: Exactly one pair of opposite sides is parallel. Therefore, QRST is a trapezoid.
b. Determine whether QRST is an isosceles trapezoid. Explain.
Answer: Since the legs are not congruent, QRST is not an isosceles trapezoid.
Example 6-3e

13. DEFG is an isosceles trapezoid with median Find DG if and
Example 6-4a

14. Subtract 20 from each side.
Theorem 8.20
Substitution
Multiply each side by 2.
Subtract 20 from each side.
Answer:
Example 6-4b

15. DEFG is an isosceles trapezoid with median Find , and if and
Because this is an isosceles trapezoid,
Example 6-4c

16. Consecutive Interior Angles Theorem
Substitution
Combine like terms.
Divide each side by 9.
Answer: Because
Example 6-4d

17. WXYZ is an isosceles trapezoid with medianb.
Answer:
Answer: Because
Example 6-4e