Question

1. find the value of the variable that results in congruent triangles. show your work.

type a response

Explanation:

Step1: Set congruent sides equal

For $\triangle ABC \cong \triangle DEF$, the corresponding sides $AC$ and $DF$ must be equal:
$9x - 6 = 5x + 10$

Step2: Isolate x terms

Subtract $5x$ from both sides:
$9x - 5x - 6 = 10$
$4x - 6 = 10$

Step3: Solve for x

Add 6 to both sides, then divide by 4:
$4x = 10 + 6$
$4x = 16$
$x = \frac{16}{4}$

Answer:

$x = 4$