Question

In the given figure, sides of ∠PQR and ∠XYZ are parallel to each other.

Prove that, ∠PQR ≅ ∠XYZ.

Answer 1

Let ray XY intersect ray QR at point M such that, X-Y-M and Q-M-R.

Ray YZ || Ray QR   ....(Given)

And line MX is their transversal.

∴ ∠XYZ ≅ ∠YMR     ....(Corresponding angle)

ray XY || ray QP     ....(Given)

ray MX || ray QP    ...(X-Y-M)

And line QR is their transversal. 

∴ ∠YMR ≅ ∠PQM         ....(Corresponding angle)

∴ ∠PQM ≅ ∠XYZ

∴ ∠PQR ≅ ∠XYZ    ....(Q-M-R)