Question

The figure below shows a parallelogram ABCD. Side AB is parallel to side DC and side AD is parallel to side BC​

A student wrote the following sentences to prove that the two pairs of parallel opposite sides of parallelogram ABCD are congruent:

For triangles ABD and CBD, alternate interior angles ABD and CBD are congruent because AB and DC are parallel lines. Alternate interior angles ADB and CBD are congruent because AD and BC are parallel lines. DB is congruent to DB by ______. The triangles ABD and CDB are congruent by ASA postulate. As corresponding parts of congruent triangles are congruent, AB is congruent to DC and AD is congruent to BC by CPCTC.

Which phrase best completes the student's proof?

a. associative property
b. reflexive property
c. substation property
d. transitive property

Answer 1

Answer: b) reflexive property

Explanation:

When you are stating that a line is congruent to itself, you are using the Reflexive Property.

a) Associative Property: a + (b + c) = (a + b) + c

b) Reflexive Property: AB = AB

c) Substation Property: not a real property - does not exist

d) Transitive Property: If a = b and b = c, then a = c