Question
If Triangle D K L is congruent to triangle P V X, which of the following statements must also be true? Check all that apply.
Triangle L K D is congruent to triangle X V P
Triangle V P X is congruent to triangle K D L
Triangle V P X is congruent to triangle D L K
Angle D is congruent to angle P
Segment D L is congruent to segment P V
Triangle L K D is congruent to triangle X V P
Triangle V P X is congruent to triangle K D L
Triangle V P X is congruent to triangle D L K
Angle D is congruent to angle P
Segment D L is congruent to segment P V
Answers
GPT-4o mini
To determine which statements must also be true given that triangle DKL is congruent to triangle PVX, we can use the properties of congruent triangles. Here are the options analyzed:
1. **Triangle LKD is congruent to triangle XV P**: This statement is **not true**. While the triangles DKL and PVX are congruent, the order of the vertices matters. The triangle LKD is the reverse order and does not necessarily maintain the same corresponding angles and sides.
2. **Triangle VPX is congruent to triangle KDL**: This statement is **true** because if DKL is congruent to PVX, then the triangles have the same angle measures and side lengths. Therefore, we can say that triangle VPX is congruent to triangle KDL.
3. **Triangle VPX is congruent to triangle DLK**: Similar to option 1, this statement is also **not true** because the order of the vertices does not maintain the necessary correspondence and thus does not imply congruence.
4. **Angle D is congruent to angle P**: This statement is **true** as a direct consequence of the congruence between the two triangles. The corresponding angles of congruent triangles are equal.
5. **Segment DL is congruent to segment PV**: This statement is also **true** since corresponding sides of congruent triangles are of equal length.
To summarize, the statements that must also be true are:
- Triangle VPX is congruent to triangle KDL
- Angle D is congruent to angle P
- Segment DL is congruent to segment PV
1. **Triangle LKD is congruent to triangle XV P**: This statement is **not true**. While the triangles DKL and PVX are congruent, the order of the vertices matters. The triangle LKD is the reverse order and does not necessarily maintain the same corresponding angles and sides.
2. **Triangle VPX is congruent to triangle KDL**: This statement is **true** because if DKL is congruent to PVX, then the triangles have the same angle measures and side lengths. Therefore, we can say that triangle VPX is congruent to triangle KDL.
3. **Triangle VPX is congruent to triangle DLK**: Similar to option 1, this statement is also **not true** because the order of the vertices does not maintain the necessary correspondence and thus does not imply congruence.
4. **Angle D is congruent to angle P**: This statement is **true** as a direct consequence of the congruence between the two triangles. The corresponding angles of congruent triangles are equal.
5. **Segment DL is congruent to segment PV**: This statement is also **true** since corresponding sides of congruent triangles are of equal length.
To summarize, the statements that must also be true are:
- Triangle VPX is congruent to triangle KDL
- Angle D is congruent to angle P
- Segment DL is congruent to segment PV