Question

question 14 of 45
in the figure below, ∠yza and ∠yzx are right angles, ∠xyz and ∠ayz are congruent, and (overline{xa}=50). what is the length of (overline{za})?

Explanation:

Step1: Identify congruent triangles

In right - triangles $\triangle YZX$ and $\triangle YZA$, $\angle YZX=\angle YZA = 90^{\circ}$, $\angle XYZ=\angle AYZ$, and $YZ$ is common to both triangles. By the Angle - Angle - Side (AAS) congruence criterion, $\triangle YZX\cong\triangle YZA$.

Step2: Use property of congruent triangles

Since $\triangle YZX\cong\triangle YZA$, corresponding sides are equal. Given that $XA = 50$, and $XA=XZ + ZA$, and $XZ = ZA$ (because of triangle congruence), then $ZA=\frac{XA}{2}$.

Step3: Calculate the length of $ZA$

$ZA=\frac{50}{2}=25$.

Answer:

C. 25