Question

(see attached photo)

The table below shows the steps to prove that if the quadrilateral ABCD is a parallelogram, then its opposite sides are congruent:


Statement: Reasons:
1 AB is parallel to DC and AD is parallel to BC -Definition of parallelogram

2 angle 1 = angle 2, angle 3 = angle 4 -If two parallel lines are cut by a transversal then the alternate interior angles are congruent

3 BD = BD -Reflexive Property

4 triangles ADB and CBD are congruent -If two angles and the included side of a triangle are congruent to the corresponding angles and side of another triangle, then the triangles are congruent by ______?_?_?_______

5 AB = DC, AD = BC -Corresponding parts of congruent triangles are congruent

Which choice completes the missing information for reason 4 in the chart?
AAS postulate
ASA postulate
HL Postulate
SAS postulate

Answer 1

Answer: ASA postulate, that is Angle-Side-Angle postulate.

Step 4 of the proof states that the triangles ADB and CBD are congruent, and the reason is that :

Angle 4 - Side BD - Angle 1 of triangle ADB are respectively equal to

Angle 3 - Side BD - Angle 2 of triangle CBD.

So we have 2 pairs of congruent angles including 2 equal sides of the triangles. This is congruence by ASA postulate.