Question

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Given: ABCD is a parallelogram.
Prove: ABCD and BC = DA
A
Proving the Parallelogram Side Theorem
B
Assemble the proof by dragging tiles to
the Statements and Reasons columns.
Angles Segments Triangles Statements Reasons
Statements
ZBAC
ZBCA
ZDAC
Reasons
ZDCA
12

Answer 1

ASA congruence theorem is applied to show that AB ≅ CD and BC ≅ DA in the parallelogram,

How to complete the proof

The two column proof is completed as follows

Statement Reason

∠ BAC ≅ ∠ DCA Alternate angles are equal

∠ BCA ≅ ∠ DAC Alternate angles are equal

AC ≅ CA Reflexive property

Δ ABC ≅ Δ ADC ASA congruence theorem

AB ≅ CD CPCTC

BC ≅ DA CPCTC