https://file.aiquickdraw.com/mathbot/file/17387626541735ulroksg.jpg

The task asks to determine whether the pairs of triangles are congruent and to state which theorem supports the answer.

Let's analyze each pair:

1. **First pair of triangles:**
   - The first triangle shows two sides marked as equal and one angle marked as equal. 
   - The second triangle shows a similar setup, with two sides and an angle marked as equal.
   - Since two sides and the included angle are equal in both triangles, we can use the **SAS (Side-Angle-Side)** Congruence Theorem to conclude that the triangles are congruent.

2. **Second pair of triangles:**
   - These two triangles share two sides that are marked as equal and the included right angle.
   - Since they have a right angle and the two sides are congruent, the **RHS (Right Angle-Hypotenuse-Side)** Congruence Theorem applies here, meaning the triangles are congruent.

3. **Third pair of triangles:**
   - In this pair, the triangles share a right angle and two sides marked as equal.
   - This corresponds to the **RHS (Right Angle-Hypotenuse-Side)** Congruence Theorem, so these triangles are congruent.

4. **Fourth pair of triangles:**
   - These triangles show two angles and one side marked as equal.
   - Since we have two angles and a side between them, we can apply the **ASA (Angle-Side-Angle)** Congruence Theorem, indicating the triangles are congruent.

5. **Fifth pair of triangles:**
   - Here, the triangles share a right angle and two sides.
   - This again follows the **RHS (Right Angle-Hypotenuse-Side)** Congruence Theorem, so these triangles are congruent.

To summarize:
- **1:** SAS Congruence Theorem
- **2:** RHS Congruence Theorem
- **3:** RHS Congruence Theorem
- **4:** ASA Congruence Theorem
- **5:** RHS Congruence Theorem

Would you like more details or clarification on any of these theorems or steps? 

---

Here are some related questions:
1. What is the difference between the SAS and ASA theorems?
2. How does the RHS theorem differ from the standard Pythagorean Theorem?
3. What happens if two triangles are congruent by SAS but not by SSS?
4. How can you prove two triangles are congruent using only angles?
5. How do you determine if triangles are congruent if only one side and one angle are known?

**Tip:** Remember, congruent triangles have exactly the same size and shape, and the congruence theorems help prove this based on certain properties like sides or angles.

Tell whether each pair of triangles is congruent or not. State the theorem that would support your answer.

Learn how to determine triangle congruence using the SAS, RHS, and ASA theorems with step-by-step solutions for each pair of triangles. This content is suitable for students in Grades 8-10, focusing on geometry and triangle properties.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation