Triangle Congruence 7Dc42D

1. **State the problem:** We have two right triangles, $\triangle YMC$ and $\triangle RZP$, with right angles at $Y$ and $Z$ respectively. 2. **Given:** The triangles are congruent by the HL (Hypotenuse-Leg) congruence theorem. 3. **HL Theorem:** Two right triangles are congruent if their hypotenuses and one corresponding leg are congruent. 4. **Identify corresponding parts:** - In $\triangle YMC$, the right angle is at $Y$, so the hypotenuse is side $MC$. - In $\triangle RZP$, the right angle is at $Z$, so the hypotenuse is side $RP$. 5. **Match hypotenuses:** $MC$ corresponds to $RP$. 6. **Match legs:** The leg with double tick marks in $\triangle YMC$ is $YM$, so it corresponds to the leg with double tick marks in $\triangle RZP$, which is $ZP$. 7. **Write congruence statement:** The order of vertices must match corresponding parts. - $Y$ corresponds to $Z$ (right angles) - $M$ corresponds to $P$ (leg with double tick marks) - $C$ corresponds to $R$ (hypotenuse) Thus, the correct congruence statement is: $$\triangle YMC \cong \triangle ZPR$$ 8. **Check options:** - $\triangle YMC \cong \triangle ZPR$ is correct. - $\triangle YCM \cong \triangle ZPR$ changes vertex order incorrectly. - $\triangle YMC \cong \triangle PZR$ reverses vertices in second triangle incorrectly. - "None of these" is incorrect. **Final answer:** $$\triangle YMC \cong \triangle ZPR$$