Question

What is the relationship between ∠BAC and ∠DAC in triangle ABC, given that m∠BAC=m∠DAC=51∘ and AB=AD=4?

Answer 1

In triangle ABC, ∠BAC and ∠DAC are congruent angles in an isosceles triangle with AB=AD=4.

Step-by-step explanation:

In triangle ABC, given that m∠BAC=m∠DAC=51° and AB=AD=4, we can determine the relationship between ∠BAC and ∠DAC. Since AB=AD, we have two congruent sides, and since ∠BAC=m∠DAC=51°, we have the angle between these two congruent sides. Therefore, triangle ABC is an isosceles triangle.

An isosceles triangle has two congruent sides and two congruent angles opposite those sides. Therefore, in triangle ABC, ∠BAC and ∠DAC are congruent angles.

So, the relationship between ∠BAC and ∠DAC is that they are congruent angles in an isosceles triangle.