Question

Given:
RS ⊥ ST
RS ⊥ SQ
∠STR ≅ ∠SQR

Prove:
△RST ≅ △RSQ

Answer 1

what grade level is that '-'

Answer 2

10th

Answer 3

Okay so, I think we consider triangles RST and RSQ:

RS is common.
Angle RST ≅ Angle RSQ (given).
Right angles at points S.

Answer 4

By the Hypotenuse-Leg Congruence Theorem (HL), if the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

Which means, △RST ≅ △RSQ by ASA (Angle-Side-Angle) congruence criterion.

Answer 5

So now we've proven that triangle RST is congruent to triangle RSQ. Or at least, should be.