https://file.aiquickdraw.com/mathbot/file/1730311620182fcilyk67.jpg

To solve this problem, let's analyze the given information and determine which congruence statement is correct.

### Given:
1. Triangle \( \triangle PKQ \) with points \( P \), \( Q \), and \( K \).
2. \( KL \) is a line that bisects \( \angle PKQ \), which means it divides \( \angle PKQ \) into two equal angles: \( \angle PKL \) and \( \angle QKL \).

### Objective:
Identify the correct congruence statement.

### Solution:
Since \( KL \) bisects \( \angle PKQ \), we know that:
- \( \angle PKL \cong \angle QKL \), as they are the two angles created by the angle bisector \( KL \).

Therefore, the correct answer is:
- **\( \angle PKL \cong \angle QKL \)**

This corresponds to the first option on the list.

### Answer:
- **\( \angle PKL \cong \angle QKL \)**

Would you like further details or have any questions?

---

Here are five related questions for further exploration:
1. What is an angle bisector, and how does it help in congruence statements?
2. How can we determine congruent triangles within a bisected angle in a triangle?
3. What other properties of triangles can be used to establish congruence?
4. How do we use Side-Angle-Side (SAS) or Angle-Side-Angle (ASA) in proving triangle congruence?
5. Why is it significant to have congruent angles when analyzing triangle properties?

**Tip:** Remember, an angle bisector divides an angle into two equal parts, which can be useful in identifying congruent triangles or angles within a shape.

Which congruence statement is true given that KL bisects ∠PKQ?

Learn how to determine the correct congruence statement for a triangle when given an angle bisector. This problem involves key concepts of congruent angles and the Angle Bisector Theorem, suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation