Question

in the diagram below, △wxy is an equilateral triangle and xz ⊥ wy. which statement must be true? a. wx = 2·xz b. wx = 2·wz c. wx = xz d. wx = wz

Explanation:

Step1: Recall equilateral - triangle property

In equilateral $\triangle WXY$, $XZ\perp WY$, so $Z$ is the mid - point of $WY$ and $\angle W = 60^{\circ}$. In right - triangle $WXZ$, $\cos W=\frac{WZ}{WX}$.

Step2: Calculate the ratio

Since $\cos60^{\circ}=\frac{1}{2}$ and $\cos W=\frac{WZ}{WX}$, we have $\frac{WZ}{WX}=\frac{1}{2}$, so $WX = 2\cdot WZ$.

Answer:

B. $WX = 2\cdot WZ$