Question

Can the two triangles be proven congruent by SAS? Explain.

A) No, there's only one pair of congruent angles, ∠B ≅ ∠D, and one pair of congruent sides, ≅ .

B) No, because the two triangles share a side.

C) Yes, because ≅ , ∠B ≅ ∠D, and and are parallel.

D) Yes, because ≅ , ∠B ≅ ∠D, and and are parallel

Answer 1

The correct option is;

Yes because AC ≅ AC, ∠B ≅ ∠D, and AD and BC are parallel.

Explanation:

Based on the the given information

The number of congruent sides = One which is AC is congruent to AC which is the reflexive property

The number of given congruent angles = One which is angle ∠ABC is congruent to ∠ADC

However, where angle ∠ABC is congruent to ∠ADC, we have AD is parallel to BC, therefore, ∠BAC is congruent to ∠DCB, and BA is parallel to CD, therefore AD is congruent to BC and DC is congruent to AB

Therefore the correct option is yes because AC ≅ AC, ∠B ≅ ∠D, and AD and BC are parallel.