https://file.aiquickdraw.com/mathbot/file/1729491169696cxmmrpjl.jpg

Let's analyze the triangles in the image to determine whether they are similar.

### Step 1: Identify Known Angles
- In **ΔLMN**:
  - ∠M = 115°
  - ∠N = 21°
  - Using the angle sum property of a triangle, we can find the missing angle ∠L:
    \[ \angle L = 180^\circ - 115^\circ - 21^\circ = 44^\circ. \]

- In **ΔPQR**:
  - ∠P = 49°
  - ∠R = 21°
  - Similarly, find the missing angle ∠Q:
    \[ \angle Q = 180^\circ - 49^\circ - 21^\circ = 110^\circ. \]

### Step 2: Compare Corresponding Angles
For two triangles to be **similar**, their corresponding angles must be equal.

- Compare:
  - ∠N (21°) = ∠R (21°) ✔
  - ∠L (44°) ≠ ∠P (49°) ✖
  - ∠M (115°) ≠ ∠Q (110°) ✖

Since not all corresponding angles are equal, **ΔLMN is not similar to ΔPQR**.

### Conclusion
The correct statement is:
- **"ΔLMN is not similar to ΔPQR."**

Would you like further clarification or have additional questions?

---

Here are 5 related questions for practice:
1. What is the Angle Sum Property of a triangle?
2. How do you determine if two triangles are similar by the AA (Angle-Angle) criterion?
3. Can triangles with equal sides but different angles be similar?
4. What other criteria can we use to test triangle similarity (e.g., SSS, SAS)?
5. How does similarity differ from congruence in triangles?

**Tip:** Always double-check that corresponding angles match when testing for similarity between triangles!

Are triangles ΔLMN and ΔPQR similar based on the given angles: ΔLMN (115°, 21°) and ΔPQR (49°, 21°)?

Learn how to determine if two triangles, ΔLMN and ΔPQR, are similar by comparing their angles. Using the Angle Sum Property and the AA criterion, find out why ΔLMN is not similar to ΔPQR. 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