Question

A conjecture and the paragraph proof used to prove the conjecture are shown.

Drag an expression or phrase to each box to complete the proof.

Answer 1

First off sorry it took me so long to respond, had some emergency. Ok now lets get on to the question.

The first box is <3.

The second box is definition of angle bisector.

The third box is <1 .

The fourth box is transitive property of congruence.

Answer 2

The correct answer is ∠1≅∠3 by the transitive property of congruence

How to Prove this Problem?

Given ABCD is parallelogram and DC bisects ∠BDE

To prove ∠1≅∠3

• It is given that ABCD is a parallelogram and So, AB is parallel DC by the definition of parallelogram so ∠1≅∠2 by alternate interior angle theorem

It is also given DC bisects ∠BDE

So, ∠2≅∠3 by definition of angle bisector

Therefore ∠1≅∠3 by the transitive property of congruence

Hence it is proved

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