Chapter 4.4, Problem 28PPS

To determine

The value of the variable that yields congruent triangles.

Answer to Problem 28PPS

Value of x = 3 yields congruent triangles.

Explanation of Solution

Given:

  $\Delta ABC\cong \Delta FGH$

  

Calculation:

According to CPCTC (Corresponding Parts of Corresponding Triangles are Congruent) $\overline{AC}\cong \overline{FH}.$

Therefore,

  $\begin{array}{l}AC=FH\\ 2x+5=11\\ 2x=11-5\\ 2x=6\\ x=6\end{array}$

The measure of line FG is:

  $\begin{array}{l}FG=4x+1\\ FG=4\left(3\right)+1\\ FG=13\end{array}$

The measure of line GH is:

  $\begin{array}{l}GH=3x-2\\ GH=3\left(3\right)-2\\ GH=7\end{array}$

This proves that $AB=FG,BC=GH$

Hence, value of x = 3 yields congruent triangles.