Theorem 7. The base angles of an isosceles trapezoid are congruent. Show Me! M Given: Isosceles Trapezoid AMOR MO//AR Prove: ZA = ZR, ZAMO = ZO 1 2 A R. E Proof: Statements Reasons 1. 1. Given 2. AM= OR; MO || AR 2. 3. From M, draw ME || OR where E lies on AR. 3. 4. Definition of a parallelogram 4. 5. ME = OR 5. 6. OR= ME 6. 7. 7. Transitive Property (SN 2 and 6) 8. AAME is an isosceles triangle. 8. 9. Z1= ZA 9. 10. Z1E ZR 10. 11. ZRE ZA 11.

Elementary Geometry For College Students, 7e
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ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Theorem 7. The base angles of an isosceles trapezoid are congruent.
Show Me!
M
Given: Isosceles Trapezoid AMOR
MO//AR
Prove: ZA = ZR, ZAMO = ZO
1 2
A
R
E
Proof:
Statements
Reasons
1.
1. Given
2. AM= OR; MO || AR
2.
3. From M, draw ME || OR where E lies on AR.
3.
4.
4. Definition of a parallelogram
5. ME= OR
6. OR=ME
6.
7.
7. Transitive Property (SN 2 and 6)
8. AAME is an isosceles triangle.
8.
9. Z1= ZA
9.
10. Z1E ZR
10.
11. ZR ZA
11.
5.
Transcribed Image Text:Theorem 7. The base angles of an isosceles trapezoid are congruent. Show Me! M Given: Isosceles Trapezoid AMOR MO//AR Prove: ZA = ZR, ZAMO = ZO 1 2 A R E Proof: Statements Reasons 1. 1. Given 2. AM= OR; MO || AR 2. 3. From M, draw ME || OR where E lies on AR. 3. 4. 4. Definition of a parallelogram 5. ME= OR 6. OR=ME 6. 7. 7. Transitive Property (SN 2 and 6) 8. AAME is an isosceles triangle. 8. 9. Z1= ZA 9. 10. Z1E ZR 10. 11. ZR ZA 11. 5.
12. ZA = ZR
12.
13. ZA and ZAMO are supplementary angles.
Z0 and ZR are supplementary angles.
13.
14. ZAMO = ZO
14.
Transcribed Image Text:12. ZA = ZR 12. 13. ZA and ZAMO are supplementary angles. Z0 and ZR are supplementary angles. 13. 14. ZAMO = ZO 14.
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