Question

Prove: AC bisects DAB and BCDIdentify the missing statement and reason in the proof.Given rhombus ABCD with diagonal AC , it follows from the definition of a rhombus that AB BC CD AD. By the reflexive property of congruence, AC = AC . So, DAC = BAC by the ?. Since corresponding parts of congruent triangles are congruent, DAC = ? and DCA = ?. So, by the definition of segment bisector AC bisects DAB and BCD .

Answer 1

Explanation:

Answer 2

To solve this question, we have that the first option is the SSS criterion since we know that when all the corresponding sides of a triangle are congruent, then both triangles are congruent.

Then, we have that: "...By the reflexive property of congruence, AC ≅ AC. So ∆DAC ≅ ∆BAC by the SSS criterion."

We can continue as follows:

"Since corresponding parts of congruent triangles are congruent, ∠DAC ≅ ∠BAC and ∠DCA ≅ ∠BCA."

In this part, we are saying that the angles are congruent to both sides of the diagonal.

In summary, we have that the options are:

1. SSS criterion

2. ∠BAC

3. ∠BCA