Given: Point A is on the bisector of angle P Q R. Prove: Point A is equidistant from the sides of angle P Q R. Art: Three rays Q P, Q A, and Q R point in rightward direction sharing a common endpoint at Q. Ray Q A is horizontal and bisects angle P Q R equally. The perpendicular from point A to ray Q P is made by a dotted line. The perpendicular cuts the ray Q P at X. Angle Q X A is labeled a right angle. The perpendicular from point A to ray Q R is made by another dotted line. The perpendicular cuts ray Q R at Y. Angle Q Y A is labeled a right angle. Drag the answers into the boxes to correctly complete the proof.

Statement Reason
1. QA−→− is the bisector of ∠PQR.
2. Response area Definition of bisector
3.∠QXA and ∠QYA are right angles. Given
4. Response area All right angles are congruent.
5. QA⎯⎯⎯⎯⎯≅QA⎯⎯⎯⎯⎯ Response area
6. Response area AAS Congruence Postulate
7. AX⎯⎯⎯⎯⎯≅AY⎯⎯⎯⎯⎯ Corresponding parts of congruent triangles are congruent.
8. Point A is equidistant from the sides of ∠PQR. Definition of equidistant