MATH SOLVE

5 months ago

Q:
# (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 parallelogram2 angle 1 = angle 2, angle 3 = angle 4 -If two parallel lines are cut by a transversal then the alternate interior angles are congruent3 BD = BD -Reflexive Property4 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 congruentWhich choice completes the missing information for reason 4 in the chart? AAS postulate ASA postulate HL Postulate SAS postulate

Accepted Solution

A:

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.

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.