Question

analyze the diagram below and complete the instructions that follow. identify the three similar right triangles in the given diagram. a. $\triangle abc, \triangle bda, \triangle bcd$ b. $\triangle abd, \triangle adc, \triangle dbc$ c. $\triangle abd, \triangle acd, \triangle dcb$ d. $\triangle adb, \triangle acd, \triangle cdb$

Explanation:

1. $\triangle ABC$ is a right triangle at $C$.
2. $\triangle BDA$ is a right triangle at $B$, $\triangle BCD$ is a right triangle at $D$.
3. By the geometric mean (altitude-on-hypotenuse) theorem, the three right triangles formed by the altitude to the hypotenuse of a right triangle are all similar to each other and the original triangle: $\triangle ABC \sim \triangle BDA \sim \triangle BCD$.

Answer:

A. $\triangle ABC, \triangle BDA, \triangle BCD$