Question

What is the missing reason in step 3 of the proof?

a)Alternate Interior Angles Theorem
Corresponding angles in congruent triangles are congruent.
b)For parallel lines cut by a transversal, corresponding angles are congruent.
c)Vertical Angles Theorem
d)SAS criterion for congruence

Answer 1

Statement Reason
1. and bisect each other. given
2. AE = EC
BE = ED definition of bisection
3. mAEB = mCED
4. ABE CDE SAS criterion
5. ACD CAB Corresponding angles of congruent triangles are congruent.
6. converse of Alternate Interior Angles Theorem
7. mBEC = mAED Vertical Angles Theorem
8. BEC DEA SAS criterion for congruence
9. DBC BDA Corresponding angles of congruent triangles are congruent.
10. converse of Alternate Interior Angles Theorem
11. Quadrilateral ABCD is a parallelogram. definition of a parallelogram