Question

1. explain why triangles wyz, wxy, and yxz are similar to one another.

Explanation:

Assuming the diagram shows right triangles (marked right angles) with shared angles:

1. For $\triangle WYZ$ and $\triangle WXY$: $\angle W$ is common, and both have a right angle ($\angle WZY = \angle WXY = 90^\circ$). By AA similarity, they are similar.
2. For $\triangle WXY$ and $\triangle YXZ$: $\angle X$ is common, and both have a right angle ($\angle WXY = \angle YXZ = 90^\circ$). By AA similarity, they are similar.
3. Transitivity of similarity: If $\triangle WYZ \sim \triangle WXY$ and $\triangle WXY \sim \triangle YXZ$, then $\triangle WYZ \sim \triangle YXZ$.

Answer:

Triangles WYZ, WXY, and YXZ are similar by AA similarity (shared angles + right angles) and transitivity.