Question

use the guide to construct a two column proof proving that triangle RST is congruent to triangle RSQ given that RS ⊥ ST, RS ⊥ SQ, and ∠STR = ∠SQR.
Given:
RS ⊥ ST
RS ⊥ SQ
∠STR = ∠SQR

Prove:
△RST ≅ △RSQ

Answer 1

They are 2 right triangles sharing the height side RS

Answer 2

angle SRT = 180 - 90 - STR = Angle SRQ sum of angles in a triangle = 180

Angle SRT = angle SQR - associative property a = b and b= c , then a= c

RS = RS ---reflexive property

Triangle RST congruent triangle RSQ ----Angle-side -angle

Answer 3

Or maybe this one,

Tan(STR) = RS / ST = tan(SQR) = RS / SQ ---- definition of a tangent

ST = SQ --- associative property a=b=c, a=c

Triangle RST congruent triangle RSQ ------side angle side congruency

Answer 4

ASA seems to work , or AAS