Question

What are the missing parts that correctly complete the proof?

Answer 1

Answer:

Definition of bisector; definition of perpendicular; ∠AXP≅∠AXQ; SAS Congruence Postulate; Corresponding parts of congruent triangles are congruent

Step-by-step explanation:

A perpendicular bisector bisects the segment it runs through; this means it splits it into two congruent segments.

A perpendicular bisector also bisects the segment at a right angle.  This makes the two angles created from the bisector and the segment right angles.

Since the angles have the same measure, they are congruent.

After the reflexive property, we have two sides and an angle between them congruent in the triangles; this means that we have the SAS congruence postulate.

Once we know the triangles are congruent, corresponding parts of congruent triangles are congruent.

Answer 2

2. PX=QX ----------- Definition of bisector.

3. AXP and AXQ ----------- Definition of perpendicular.

4. AXP=AXQ ------------- All right angles are congruent.

6. AXP=AXQ ------------ SAS congruence 

7. AP=AQ -------------Corresponding parts of congruent triangles

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