Question

What are the missing statement and reason in step 2 of the proof? Statement: ∠ABC ≅ ∠BCD, ∠BAD ≅ ∠ADC Reason: For parallel lines cut by a transversal, corresponding angles are congruent. Statement: ΔABC ≅ ΔCDA Reason: SSS criterion for congruence Statement: AB ≅ CD, BC ≅ AD Reason: given Statement: AB ∥ CD, BC ∥ AD Reason: definition of a parallelogram Statement: ∠BAC ≅ ∠ACD Reason: Alternate Interior Angles Theorem

Answer 1

Answer:

Statement: AB=CD, BC=AD

Reason: By definition of parallelogram .

Statement: AC=AC

Reason: Reflexive property of equality.

Step-by-step explanation:

1.Statement: $\angle ABC\cong \angle BCD,\angle BAD\cong \angle ADC$.

Reason: For parallel lines cut by a transversal , corresponding angles are congruent.

2.Statement:AB=CD,BC=AD

Reason: By definition of parallelogram.

3.Statement: AC=AC

Reason: Reflexive property of equality.

4.Statement: $\triangle ABC\cong \triangle CDA$.

Reason: SSS criterion for congruence.

5.Statement:$AB\cong CD, BC\cong AD$.

Reason: Given .

6.Statement: $AB\parallel CD, BC\parallel AD$.

Reason: By definition of parallelogram.

7.Statement: $\angle BAC\cong \angle ACD$.

Reason: Alternate Interior Angles Theorem.

Answer 2

The missing statement and reason in step 2 in the proof are:

B. Statement: AB∥CD, BC∥AD

Reason: definition of a parallelogram

What is a Parallelogram?

A paralleogram is a quadrilateral that has two pairs of opposite sides that are parallel to each other.

In step 2, since AB ∥ CD, and BC ∥ AD, it means that quadrilateral ABCD is a parallelogram.

Thus, the missing statement and reason are therefore:

B. Statement: AB∥CD, BC∥AD

Reason: definition of a parallelogram

Learn more about parallelogram on:

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