https://file.aiquickdraw.com/mathbot/file/1729210336800em40xkmj.jpg

In this image, we are given two triangles, \( \triangle MNP \) and \( \triangle QST \), and the task is to determine which postulate or theorem can be used to prove their congruence.

### Given information:
- In \( \triangle MNP \), segment \( MP \) is congruent to segment \( QS \).
- Angle \( \angle M \) is congruent to angle \( \angle Q \).
- Segment \( NP \) is congruent to segment \( ST \).

### Conclusion:
This situation provides us with two sides and the included angle between them. This is a classic application of the **SAS (Side-Angle-Side) Congruence Postulate**, which states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the triangles are congruent.

Thus, the triangles \( \triangle MNP \) and \( \triangle QST \) are congruent by the **SAS postulate**.

Would you like more details or have any further questions?

Here are some related questions you may find useful:
1. What are other congruence postulates besides SAS?
2. How do you determine when to apply each congruence postulate?
3. What happens if only one pair of sides and angles are congruent?
4. Can congruence be proven using angles only?
5. How is the SAS postulate different from the ASA (Angle-Side-Angle) postulate?

**Tip:** Always check if the given information aligns with one of the common congruence postulates (SSS, SAS, ASA, AAS, or HL).

Determine which postulate can be used to prove that the triangles are congruent or if not possible.

Learn how to determine triangle congruence for triangles MNP and QST using the SAS (Side-Angle-Side) postulate. This problem explores triangle congruence postulates and is suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation