1) QA is the bisector of ∠PQR Given
2) m ∠ PQA = m ∠ RQA Definition of Bisector
3) ∠QXA and ∠QYA are right Given
4) m ∠QXA = m ∠ QYA All right angles are congruent
(Also, since m ∠QXA = 90 degrees and m ∠QYA = 90 degrees, you can say Transitive Property here)
5) QA = QA Reflexive Property
6) ΔQXA = ΔQYA AAS Congruence
(Angle - Angle - Side, with QA in common in both triangles)
7) AX = AY CPCTC
(Corresponding parts of congruent triangles are congruent)
8) A is equidistant Definitiion of equidistant
The missing statements and proofs that complete the proof in the question are;
Statement 2; m∠ PQA = m∠ RQA
Statement 4; m∠ QXA = m∠ QYA
Statement 6; ΔQXA = ΔQYA
Reason 1; Given.
Reason 5; Reflexive Property
The statements and reasons that give the proof are;
Statement 1; QA is the bisector of ∠PQR
Reason 1; The reason is because we are Given.
Statement 2; m∠ PQA = m∠ RQA
Reason 2; Definition of Bisector
Statement 3; ∠QXA and ∠QYA are right angles.
Reason 3; Given
Statement 4; m∠ QXA = m∠ QYA
Reason 4; All right angles are congruent
Statement 5; QA = QA
Reason 5; Reflexive Property
Statement 6; ΔQXA = ΔQYA
Reason 6; AAS Congruence Postulate
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