Elementary Geometry for College Students (6th Edition)

Proof for the problem: 1. $\angle R$ and $\angle V$ are right $\angle$s (1. Given) 2. $\triangle RST$ and $\triangle VST$ are right triangles. (2. A triangle that has one right angle is a right triangle) 3. $\overline{ST}\cong\overline{ST}$ (3. Identity) 4. $\overline{RT}\cong\overline{VT}$ (4. Given) 5. $\triangle RST\cong\triangle VST$ (5. HL)
1) First, it is given that $\angle R$ and $\angle V$ are right $\angle$s. So, $\triangle RST$ and $\triangle VST$ are right triangles. 2) It is also given that $\overline{RT}\cong\overline{VT}$ 3) By identity, we find that $\overline{ST}\cong\overline{ST}$ Now we see that the leg and hypotenuse of right $\triangle RST$ are congruent with the leg and hypotenuse of right $\triangle VST$. So we would use HL to prove triangles congruent. Now we would construct a proof for the problem: 1. $\angle R$ and $\angle V$ are right $\angle$s (1. Given) 2. $\triangle RST$ and $\triangle VST$ are right triangles. (2. A triangle that has one right angle is a right triangle) 3. $\overline{ST}\cong\overline{ST}$ (3. Identity) 4. $\overline{RT}\cong\overline{VT}$ (4. Given) 5. $\triangle RST\cong\triangle VST$ (5. HL)