Question

in the diagram, $overline{bc}congoverline{ef}$ and $angle a$ and $angle d$ are right angles. for the triangles to be congruent by hl, what must be the value of $x$? 8 9 17 34

Explanation:

Step1: Recall HL congruence criterion

HL (Hypotenuse - Leg) states that for two right - triangles, if the hypotenuses are congruent and one pair of legs are congruent, the triangles are congruent. Here, $\overline{BC}\cong\overline{EF}$ (hypotenuses) and we need to set the legs equal. So, $34 = 4x+2$.

Step2: Solve the equation for x

Subtract 2 from both sides of the equation: $34 - 2=4x+2 - 2$, which simplifies to $32 = 4x$. Then divide both sides by 4: $\frac{32}{4}=\frac{4x}{4}$, so $x = 8$.

Answer:

8