Question 1: Since the triangles are congruent, we know that QS = TV This means that 3v + 2 = 7v - 6 Subtract both sides by 2 3v = 7v - 8 Subtract 7v from both sides -4v = -8 Divide both sides by -4 v = 2 Plug this value back into 3v + 2 and you get 8. QS = 8 Since the triangles are congruent QS = 8 AND TV = 8
Question 2: So we know that AC = AC because that's a shared side. It's also given that BC = CD. In order for two triangles to be congruent by SAS, the angle between the two sides must be congruent. That means angle C must be congruent to angle C from the other triangle.
Question 3: We know that AC = AC because it's a shared side. We also know that angle A from one triangle is equal to angle C from the other. However, for a triangle to be congruent by SAS, the congruent angle must be between two congruent sides. In order for us to prove congruence by SAS, AD must be congruent to BC.
