Question

14.1 figur 13. Opposite sides of a parallelogram are parallel Prove that opposite angles of a parallelogram are congruent. Nam Glven: ABCD is a parallelogram Prove: ZA A ZC, 2BA 2D Statements Reasons 1. AB II CD 2. m2B+ m2cm 180 mzA+ m2D - 180 2 3. BC || AD 3. 4. m2A + m2B = 180 m2C + m2D - 180 4. M m21 5. MZA+ m2B = m2B + m2c 5. 6. 6. MzA - mac m22 m23 7. ZANZC 7. m24 8. m2B + m2 m2C+ m2D 8. 9. m2B = m2D 9. 10. 2B SZD 10

Answer 1

Required: To prove that opposite angles of a parallelogram are congruent.

$\text{Prove: }\angle A\cong\angle C,\text{ }\angle B\cong\angle D$

1. Given ( opposite sides of a parallelogram are parallel)

2. Adjacent angles of a parallelogram are supplementary.

3. Given (opposite of a parallelogram are parallel)

4. Adjacent angles of a parallelogram are supplementary.

5. Congruency property

6. Transitive property

7. Congruency

8. Transitive property

9. Transitive property

10. Congruency