5. if $ \triangle prs \cong \triangle cfh $, find the values of $ x, y $, and $ z $.
$ x= $
$ y= $
$ z= $

Question

Accepted Answer

# Explanation:
## Step1: Use the property of congruent triangles (corresponding sides and angles are equal)
Since $\triangle PRS\cong\triangle CFH$, then $PS = FH$, $ \angle P=\angle C$, $ \angle R=\angle H$.
For the side - length: $PS = 2x - 7$ and $FH = 24$, so $2x-7 = 24$.
## Step2: Solve the equation for $x$
$$
\begin{align*}
2x-7&=24\
2x&=24 + 7\
2x&=31\
x&=\frac{31}{2}=15.5
\end{align*}
$$
## Step3: Solve for $y$ using the angle - equality
$\angle R=13y - 1$ and $\angle H = 42-4$. Since $\angle R=\angle H$, then $13y-1=42 - 4$.
$$
\begin{align*}
13y-1&=38\
13y&=38 + 1\
13y&=39\
y&=3
\end{align*}
$$
## Step4: Solve for $z$ using the angle - equality
$\angle P = 28^{\circ}$, $\angle C=z$. Since $\angle P=\angle C$ (corresponding angles of congruent triangles), then $z = 28$.

# Answer:
$x = 15.5$, $y = 3$, $z = 28$

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QUESTION IMAGE

Question

Explanation:

Step1: Use the property of congruent triangles (corresponding sides and angles are equal)

Step2: Solve the equation for \(x\)

Step3: Solve for \(y\) using the angle - equality

Step4: Solve for \(z\) using the angle - equality

Answer: