| Statements | Reasons |
| 1. XQ¯ || TR¯ | 1. Given |
| 2. ∠Q ≅ ∠T | 2. Alternate Interior Angles Theorem |
| 3. ∠X ≅ ∠R | 3. Alternate Interior Angles Theorem |
| 4. XR¯ bisects QT¯ | 4. Given |
| 5. TM¯ ≅ QM¯ | 5. Definition of segment bisector |
| 6. ΔXMQ ≅ ΔRMT | 6.? |
A.
B.
C.
D.
Step 1: If the two angles and the non-included side of one triangle are congruent to the two angles and the non-included side of another triangle, then the two triangles are congruent.[AAS Theorem.]
Step 2: As ∠Q ≅ ∠T, ∠X ≅ ∠R and TM¯
≅ QM¯, by AAS Theorem, we have ΔXMQ ≅ ΔRMT.