https://file.aiquickdraw.com/mathbot/file/1730311227059lszd0ldk.jpg

From the image, I see two triangles: △JKL and △EFG. Below them, you are asked to complete several congruence statements and determine whether the triangles are congruent.

Let's break this down step by step:

---

### (a) Congruent Angles:
We need to match corresponding angles between the two triangles:

- **∠J** corresponds to **∠E** (both are at the left bottom vertex).
- **∠K** corresponds to **∠F** (both are the lower interior angle near the short side).
- **∠L** corresponds to **∠G** (both are the angle opposite the longest side).

So the answers will be:
- ∠J ≅ ∠E
- ∠K ≅ ∠F
- ∠L ≅ ∠G

---

### (b) Congruent Sides:
Now, we determine which sides correspond:

- **JK** corresponds to **EF** (shortest side).
- **KL** corresponds to **FG** (medium-length side).
- **JL** corresponds to **EG** (longest side).

So the answers will be:
- JK ≅ EF
- KL ≅ FG
- JL ≅ EG

---

### (c) Are the triangles congruent?
If all three pairs of corresponding angles are congruent, and all three pairs of corresponding sides are congruent, then the triangles are congruent.

Answer: **Yes, and the triangles are congruent.**

---

Let me know if any part of this needs further clarification. 

---

**Follow-up Questions:**
1. What are the different criteria for proving triangle congruence (e.g., SSS, SAS, ASA)?
2. Can two triangles have congruent angles but different side lengths?
3. What is the difference between congruence and similarity of triangles?
4. How can you use the Pythagorean theorem to confirm side congruence?
5. How does the angle-side relationship affect triangle properties?

**Tip:** When comparing triangles, always match the vertices in the same order to avoid mistakes.

Based on the image of triangles △JKL and △EFG, complete the congruence statements for angles and sides, and determine if the triangles are congruent.

Learn how to complete congruence statements for triangles △JKL and △EFG by identifying congruent angles and sides, and determine if the triangles are congruent. Covers essential concepts in geometry, including angle and side congruence.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation