Left Panel Interactive

Statements

Reasons

1. ∠A ≅ ∠C; ∠B ≅ ∠D

1. given

2. m∠A = m∠C; m∠B = m∠D

2. def. of congruent angles

3. Draw AC

3. unique line postulate

4. m∠D + m∠1 + m∠3 = 180°

4. sum of measures of interior angles of a triangle is 180°

5. m∠B + m∠2 + m∠4 = 180°

5. sum of measures of interior angles of a triangle is 180°

6. m∠D + m∠1 + m∠3 = m∠B + m∠2 + m∠4

6. transitive property

7. m∠1 + m∠3 =
m∠2 + m∠4

7. subtraction property

8. m∠1 + m∠2 = m∠A; m∠3 + m∠4 = m∠C;

8. angle addition postulate

9. m∠1 + m∠2 =
m∠3 + m∠4

9. substitution property

10. m∠1 + m∠3 = m∠2 + m∠4
−(m∠1 + m∠2 = m∠3 + m∠4)
m∠3 − m∠2 = m∠2 − m∠3

10. subtraction

11. 2m∠3 = 2m∠2

11. addition property

12. m∠3 = m∠2

12. division property

13. ∠3 ≅ ∠2

13. def. of congruent

14. AB || DC

14. converse of alternate interior angles theorem

15. AD || BC

15. similar argument

16. ABCD is a parallelogram

16. def. of parallelogram