Questions: Given: angle R is congruent to angle Q line segment AS is congruent to line segment AT Which of the following may not be true? - angle 2 is congruent to angle 3 - line segment RS is congruent to line segment TQ - angle 5 is congruent to angle 6 - line segment AR is congruent to line segment AQ

Solution Steps

The problem states the following:

• $\angle R \cong \angle Q$
• $\angle S \cong \angle T$

Given the congruent angles, we can infer that triangles $\triangle RAS$ and $\triangle QAT$ are isosceles triangles with the following properties:

• $\angle R = \angle Q$
• $\angle S = \angle T$

We need to determine which of the given options may not be true based on the given information.

1. $\angle 2 = \angle 3$

   • This is true because $\angle 2$ and $\angle 3$ are corresponding angles in the isosceles triangles.

2. $RS = TQ$

   • This is true because $RS$ and $TQ$ are corresponding sides in the isosceles triangles.

3. $\angle 5 = \angle 6$

   • This is true because $\angle 5$ and $\angle 6$ are corresponding angles in the isosceles triangles.

4. $AR \cong AQ$

   • This may not be true because there is no information given that $AR$ and $AQ$ are congruent.

Final Answer