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