In figure 2.8, sides of ∠ PQR and ∠XYZ are parallel to each other. prove that, ∠ PQR ≅ ∠ XYZ

Given ∠ PQR AND ∠XYZ are parallel and also YZ and QR are parallel

TO find: ∠ PQR ≅ ∠ XYZ

Construction: extend sag XY such that Q-S-R.

PQ|| XY (given)

PQ || XS and QR is transversals (from construction)

∠ PQR ≅ ∠ XSR (corresponding angle theorem) if two parallel line are cut by a transversal, then the pairs of corresponding angle are congruent) ………………………. (1)

YZ||SK and XS is transversals (given)

∠ XYZ ≅ ∠ XSR (corresponding angle theorem) if two parallel line are cut by a transversal, then the pairs of corresponding angle are congruent.) …………………………(2)

Equation (1) and (2) right side is equal

So that, ∠ PQR≅ ∠ XYZ hence proved.