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.