Question

The proof shows that opposite angles of a parallelogram are congruent. Given: ABCD is a parallelogram with diagonal AC. Prove: ∠ BAD ≅ ∠ DCB What is the missing reason In this partial proof? Question 3 options:
ASA Substution Angle Angle Postulate Alternate Interior Angles are Congruent

Answer 1

A parallelogram is a figure which has its opposite sides to be equal and parallel. The missing reason in the proof is:

B. Substitution Angle Angle Postulate.

A parallelogram is a type of quadrilateral that has its opposite sides to be equal and parallel. The sum of its internal angles is $360^{o}$.

To prove that ∠ BAD ≅ ∠ DCB, we have:

Given parallelogram ABCD;

<BAC ≅ <ACD (alternate angle theorem)

<DAC ≅ <ACB (alternate angle theorem)

<BAC + <DAC = <BAD

Also,

<BCA + <DCA = <BCD

Therefore,

<BAD ≅ <DCB (Substitution Angle Angle Postulate)

Thus, the missing reason in the partial proof is:

option B. Substitution Angle Angle Postulate

A sketch is attached to this question for more clarifications.

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