Question

1. $\triangle wxy \cong \triangle zyx$ solve for $p$ and $q$.
2. the perimeter of $abcd$ is 85. if $\triangle abc \cong \triangle adc$, find the value of $x$.
3. solve for $x$.
4. if $\triangle efg \cong \triangle hjk$, complete each part.

a) $\overline{eg} \cong$
b) $\overline{hj} \cong$
c) $\angle f \cong$
d) $\angle h \cong$
e) $\triangle fge \cong$

1. if $d$, $e$, and $f$ are midpoints of the sides of $\triangle abc$, find the perimeter of $\triangle abc$

Explanation:

Step1: Use the property of congruent triangles

Since \(\triangle WXY\cong\triangle ZYX\), corresponding sides are equal.
For side \(WX\) and \(ZY\): \(7p + 13=20\)
For side \(WY\) and \(ZX\): \(2q + 3=11\)

Step2: Solve the equation for \(p\)

\(7p+13 = 20\)
Subtract \(13\) from both sides: \(7p=20 - 13\)
\(7p=7\)
Divide both sides by \(7\): \(p = 1\)

Step3: Solve the equation for \(q\)

\(2q+3 = 11\)
Subtract \(3\) from both sides: \(2q=11 - 3\)
\(2q=8\)
Divide both sides by \(2\): \(q = 4\)

Answer:

\(p = 1\), \(q = 4\)