https://file.aiquickdraw.com/mathbot/file/1726079081097hagd0409.jpg

The question asks to determine the congruence criteria for triangles \( \triangle ABC \) and \( \triangle PQR \), based on the provided information:

- \( AB = PQ \)
- \( \angle A = \angle P \)
- \( \angle DCA = \angle SRP \)

From this, let's break it down:

1. **Side \( AB = PQ \)**: The corresponding sides in the two triangles are equal.
2. **Angle \( \angle A = \angle P \)**: The corresponding angles at vertices \( A \) and \( P \) are equal.
3. **Angle \( \angle DCA = \angle SRP \)**: These are corresponding angles in both triangles (formed by the intersections at \( C \) and \( R \)).

Thus, we have **two angles and one side** (the side between two angles is the included side). This matches the **ASA (Angle-Side-Angle)** congruence rule.

The correct answer is:
**(b) ASA**

Would you like any further explanation? Here are 5 related questions that expand on this concept:

1. What are the differences between the ASA and SAS congruence criteria?
2. How would the congruence criteria change if another side was given instead of an angle?
3. What does the AAS (Angle-Angle-Side) rule state, and how does it differ from ASA?
4. If two triangles share all angles but not sides, can they still be congruent?
5. How can you determine whether triangles are congruent using the RHS (Right angle-Hypotenuse-Side) rule?

**Tip:** In congruence criteria, always check if the information relates to angles or sides, and note their arrangement (whether the side is between the angles).

In the given figure, AB = PQ, ∠A = ∠P, and ∠DCA = ∠SRP. Then, ΔABC ≅ ΔPQR is congruent by _____ congruence criteria.

Learn how to determine triangle congruence using the ASA (Angle-Side-Angle) rule. The problem asks to prove the congruence of two triangles based on given angles and sides. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation