Question

Given ∠C≈∠B and ∠BDA is a right angle, are the two triangles △BDA and △CDA similar? If so, by what criterion?

a. SAS (Side-Angle-Side)
b. AAA (Angle-Angle-Angle)
c. SSS (Side-Side-Side)
d. ASA (Angle-Side-Angle)

Answer 1

Two triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional. Given that ∠C$≈∠B$ and ∠BDA is a right angle, the two triangles △BDA and △CDA are similar by the AAA (Angle-Angle-Angle) criterion.

Step-by-step explanation:

Two triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional.

Given that ∠C$≈∠B$ and ∠BDA is a right angle, we can determine if the triangles △BDA and △CDA are similar.

To determine the similarity between the two triangles, we can use the AAA criterion (Angle-Angle-Angle). Since ∠C$≈∠B$ and ∠BDA is a right angle, we have two pairs of corresponding congruent angles. Therefore, the two triangles are similar by AAA criterion.