Question

triangle abc is a right triangle with altitude cd. move options to the blanks to prove that △abc ~ △acd and △abc ~ △cbd. because right angles are congruent, ∠bca ≅ ∠cda. by the reflexive property, ∠a ≅ ____. thus, △abc ~ __ by the __ postulate. because right angles are congruent, ∠bca ≅ ∠bdc. by the reflexive property, ∠b ≅ __. finally, △abc ~ __ by the ____ postulate. ∠a, ∠b, ∠bca, ∠bdc, ∠cda, △acd, △cbd, angle - angle, side - angle - side

Explanation:

Step1: Apply reflexive property for ∠A

By the reflexive property, an angle is congruent to itself. So, $\angle A\cong\angle A$.

Step2: Determine similar - triangle for first pair

Since $\angle BCA\cong\angle CDA$ (right - angles are congruent) and $\angle A\cong\angle A$, by the Angle - Angle (AA) Postulate, $\triangle ABC\sim\triangle ACD$.

Step3: Apply reflexive property for ∠B

By the reflexive property, $\angle B\cong\angle B$.

Step4: Determine similar - triangle for second pair

Since $\angle BCA\cong\angle BDC$ (right - angles are congruent) and $\angle B\cong\angle B$, by the Angle - Angle (AA) Postulate, $\triangle ABC\sim\triangle CBD$.

Answer:

First row: $\angle A$; $\triangle ACD$; Angle - Angle
Second row: $\angle B$; $\triangle CBD$; Angle - Angle