Given: and bisect each other.
prove: quadrilateral abcd is a parallelogram.
proof:
statement reason
1. and bisect each other. given
2. ae = ec
be = ed definition of bisection
3. m∠aeb = m∠ced
4. δabe ≅ δcde sas criterion
5. ∠acd ≅ ∠cab corresponding angles of congruent triangles are congruent.
6. converse of alternate interior angles theorem
7. m∠bec = m∠aed vertical angles theorem
8. δbec δdea 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
9
what is the reason for step 3 of this proof?
a.
alternate interior angles theorem
b.
corresponding angles in congruent triangles are congruent.
c.
for parallel lines cut by a transversal, corresponding angles are congruent.
d.
vertical angles theorem
e.
sas criterion for congruence