Question

According to the diagram below, which similarity statements are true?

Answer 1

Answer: C. $\triangle{ABC}\sim\triangle{ADB}$

D. $\triangle{ABC}\sim\triangle{BDC}$

Step-by-step explanation:

Given:  $\triangle{ABC}$ is a right triangle in with BD is an altitude.

Now, in $\triangle{ABC}$ and  $\triangle{ADB}$, we have

$\angle{A}=\angle{A}$ [common]

$\angle{ABC}=\angle{BDA}=90^{\circ}$

By AA- similarity postulate , we have

$\triangle{ABC}\sim\triangle{ADB}$

Similarly,  in $\triangle{ABC}$ and  $\triangle{BDC}$, we have

$\angle{C}=\angle{C}$  [common]

$\angle{ABC}=\angle{BDC}=90^{\circ}$

By AA- similarity postulate , we have

$\triangle{ABC}\sim\triangle{BDC}$

In $\triangle{BDC}$ and  $\triangle{ADB}$ only one angle is given equal . so we cannot apply any similarity postulate to show them similar.

Answer 2

Based on the right triangle similarity theorem, the similarity statements that are true are:

A. ΔABD ~ ΔBCD

C. ΔABC ~ ΔADB

What is the Right triangle Similarity Theorem?

The right triangle similarity theorem states that when an altitude intersects the hypotenuse of a right triangle, the two two triangles that are formed are similar to each other and also to the original triangle.

Thus, in the image given showing a right triangle with an altitude, the three triangle are all similar to each other.

Therefore, based on the right triangle similarity theorem, the similarity statements that are true are:

A. ΔABD ~ ΔBCD

C. ΔABC ~ ΔADB

Learn more about right triangle similarity theorem on:

https://brainly.com/question/10264412