Question

for the triangles to be congruent by hl, what must be the value of x? 2 3 4 7

Explanation:

Step1: Apply HL - Hypotenuse - Leg theorem

For right - triangles to be congruent by HL, the hypotenuses and one pair of legs must be equal. Let's assume the hypotenuse of the first triangle \(AC = 15\) is equal to the hypotenuse of the second triangle \(FH=3x + 3\), and leg \(AB = 9\) is equal to leg \(FG=2x + 1\). We'll set up the equation based on the equality of the hypotenuses: \(3x+3 = 15\).

Step2: Solve the equation for \(x\)

Subtract 3 from both sides of the equation \(3x+3 = 15\):
\[3x+3−3=15 - 3\]
\[3x=12\]
Divide both sides by 3:
\[\frac{3x}{3}=\frac{12}{3}\]
\[x = 4\]
We can also check with the other pair of legs. If \(x = 4\), then \(2x+1=2\times4 + 1=9\) which satisfies the HL congruence condition.

Answer:

4