Question

In figure, sides of $\angle PQR$ and $\angle XYZ$ are parallel to each other. Prove that, $\angle PQR\cong \angle XYZ$

Answer 1

Here,

$PQ\parallel XY$ and $PQ=XY$

$PR\parallel XZ$ and $PR=XZ$

Taking $\Delta PQR$ and $\Delta XYZ$,

$PQ=XY$

$PR=XZ$

$\angle QPX=\angle YXM=a$

$\angle RPX=\angle ZXM=b$

$\angle XYZ=\angle YXM+\angle ZXM=a+b$

$\angle XYZ=\angle QPR=a+b$

$\Rightarrow \Delta PQR\cong \Delta XYZ$

Hence, proved.