Question

Triangle R S T is shown with base angles R and T .An angle bisector is drawn from vertex S to side R T. The point where it intersects R T is labeled P.
Given: ΔRST with ∠R≅∠T

Prove: RS¯¯¯¯¯¯¯≅ST¯¯¯¯¯¯¯

Read the statements of proof, then answer the question.

Statements Reasons
1. ∠R≅∠T 1. Given
2. Draw SP¯¯¯¯¯¯¯ such that it bisects ∠S 2. Construction
3. ∠RSP≅∠PST 3.
4. SP¯¯¯¯¯¯¯≅SP¯¯¯¯¯¯¯ 4.
5. △RSP≅△TSP 5.
6. RS¯¯¯¯¯¯¯≅ST¯¯¯¯¯¯¯ 6.
What reason justifies statement 3?

(1 point)
Responses

Corresponding angles are congruent.
Corresponding angles are congruent.

Angles formed by a bisector are congruent.
Angles formed by a bisector are congruent.

Alternate interior angles are congruent.
Alternate interior angles are congruent.

Vertical angles are congruent.

Answer 1

The reason that justifies statement 3, where it states that \( \angle RSP \cong \angle PST \), is:

**Angles formed by a bisector are congruent.**

This is because by the definition of an angle bisector, it divides the angle into two equal angles. Therefore, \( \angle RSP \) and \( \angle PST \) are congruent as they are the two angles formed by the bisector \( SP \).