in the diagram, $overline{bc}congoverline{ef}$ and $angle a$ and $angle d$ are right angles. for the…
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
Answer
Explanation:
Step1: Recall HL - Hypotenuse - Leg theorem
For right - angled triangles to be congruent by HL, the hypotenuses must be equal. Given $\overline{BC}\cong\overline{EF}$, and in right - triangles $\triangle ABC$ and $\triangle DEF$ with right angles at $\angle A$ and $\angle D$ respectively, the hypotenuses are 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