Question

If Triangle Q S R is congruent to triangle Y X Z describes two triangles, which other statement is also true?
Triangle Q R S is congruent to Triangle X Y Z
Triangle Q R S is congruent to Triangle Y Z X
Triangle Q R S is congruent to Triangle Z X Y
Triangle Q R S is congruent to Triangle X Z Y

Answer 1

If triangle \( QSR \) is congruent to triangle \( YXZ \), it means that the corresponding angles and sides of the two triangles are equal. The corresponding vertices are typically matched in the order they are stated, which means:

- \( Q \) corresponds to \( Y \)
- \( S \) corresponds to \( X \)
- \( R \) corresponds to \( Z \)

To find congruent triangles from the options given, we can look for the correct order of vertices:

1. **Triangle QRS is congruent to Triangle XYZ**.
2. **Triangle QRS is congruent to Triangle YZX** (since the labels of the vertices can rotate).
3. **Triangle QRS is NOT congruent to Triangle ZXY** (this does not maintain the correct correspondences).
4. **Triangle QRS is NOT congruent to Triangle XZY** (this also does not maintain correct correspondences).

The only statements that maintain congruency based on the vertex correspondences are:

- **Triangle QRS is congruent to Triangle YXZ** (the original statement)
- **Triangle QRS is congruent to Triangle YZX** (as it just rearranges the same angles/sides).

So the answer is:

**Triangle Q R S is congruent to Triangle Y Z X.**