In the figure shown on the right, PR ⊥ RQ, ST ⊥ RQ, and SQ ⊥ PS, Prove that ∠𝑃 ≅ ∠Q and ∠𝑅𝑉𝑃 ≅ ∠QST.

Question

Answer 1

First of all, you need to draw the figure to reflect what is given: QSV is a right angle, not an obtuse angle as suggested in the figure.

Triangle PRV is similar to triangle QSV...vertical angles are equal then 2 right triangles with one acute acute angle equal

That makes angle P = angle Q .... similar triangles have equal angles

Angle RVP is complementary to angle P and angle QST is complementary to angle Q; therefore angle RVP and angle QST are equal because they are complementary to equal angles.