Question

δbcd and δfed are shown below. which statement is true? δbcd is similar to δfed. δbcd is not similar to δfed. there is not enough information to determine whether the triangles are similar.

Explanation:

Step1: Find the third angle of $\triangle BCD$

In $\triangle BCD$, we know that one angle is $90^{\circ}$ (right - angle at $C$) and another is $49^{\circ}$. Using the angle - sum property of a triangle ($\angle B+\angle C+\angle BDC = 180^{\circ}$), the third angle $\angle BDC=180^{\circ}-(90^{\circ} + 49^{\circ})=41^{\circ}$.

Step2: Check for similarity

In $\triangle BCD$ and $\triangle FED$:

• $\angle C=\angle E = 90^{\circ}$ (right - angles)
• $\angle BDC=\angle FDE = 41^{\circ}$ (common angle)

By the AA (Angle - Angle) similarity criterion (if two angles of one triangle are equal to two angles of another triangle, then the two triangles are similar), $\triangle BCD\sim\triangle FED$.

Answer:

$\triangle BCD$ is similar to $\triangle FED$.