Question

The figure below shows a parallelogram ABCD. Side AB is parallel to side DC and side AD is parallel to side BC: A quadrilateral ABCD is shown with the two pairs of opposite sides AD and BC and AB and DC marked parallel. The diagonal are labeled BD and AC A student wrote the following sentences to prove that parallelogram ABCD has two pairs of opposite sides equal: For triangles ABD and CDB, alternate interior angle ABD is congruent to angle CDB because AB and DC are parallel lines. Similarly, alternate interior angle ADB is equal to angle CBD because AD and BC are parallel lines. DB is equal to DB by reflexive property. Therefore, triangles ABD and CDB are congruent by _______________. Therefore, AB is congruent to DC and AD is congruent to BC by CPCTC. Which phrase best completes the student's proof? ASA Postulate HL Postulate SAS Postulate SSS Postulate

Answer 1

Answer: ASA postulate

Step-by-step explanation:

According to the ASA (Angle-Side-Angle) postulate, if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent to each other. '

Here Given: ABCD is a parallelogram

That is, AB ║ CD and AD ║ BC

We have to prove that:The parallelogram ABCD has two pairs of opposite sides equal, that is, AB ≅ CD and AD ≅ BC.

Here BD is the diagonal of the parallelogram ABCD ( shown in the below figure)

Thus, In Δ ABD and Δ CBD

∠ABD ≅ ∠CDB ( alternative interior angles made on parallel lines by the same transversal BD)

BD ≅ BD ( Reflexive )

And, ∠ADB ≅ ∠CBD (  alternative interior angles made on parallel lines by the same transversal BD)

Here, Two angles and the included side of triangle ADB are congruent to two angles and included side of traingle BCD.

Therefore, By ASA postulate of congruence,

Δ ABD ≅ Δ CBD

Thus, By CPCTC, AB ≅ CD and AD ≅ BC.

Answer 2

Answer:

ASA postulate

Step-by-step explanation: