Question

in the figure shown, what is the value of x?
x =
13x - 12
(7x - 6)

Explanation:

Step1: Identify congruent triangles

By the Side - Angle - Side (SAS) congruence criterion, \(\triangle ABC\cong\triangle DEF\). So, \(BC = EF\).

Step2: Set up the equation

Since \(BC = 13x - 12\) and \(EF=7x - 6\), we have the equation \(13x - 12=7x - 6\).

Step3: Solve the equation

Subtract \(7x\) from both sides: \(13x-7x - 12=7x - 7x- 6\), which simplifies to \(6x-12=-6\).
Add \(12\) to both sides: \(6x-12 + 12=-6 + 12\), so \(6x = 6\).
Divide both sides by \(6\): \(x=\frac{6}{6}=1\).

Answer:

\(1\)