Question

What are the missing parts that correctly complete the proof?

a. Statement: "A is equidistant from the sides of angle PQR."
Reason: "Angle bisectors create congruent angles."
b. Statement: "A is equidistant from the sides of angle PQR."
Reason: "A is on the angle bisector of PQR."
c. Statement: "A is equidistant from the sides of angle PQR."
Reason: "P, Q, and R are collinear."
d. Statement: "A is equidistant from the sides of angle PQR."
Reason: "A is equidistant from P, Q, and R."

Answer 1

The correct proof statement involves a point being equidistant from the sides of an angle PQR because the point lies on the angle bisector of PQR.

The correct option is d.

Step-by-step explanation:

The correct completion for the proof that involves a point being equidistant from the sides of an angle is:

Statement: "A is equidistant from the sides of angle PQR."
Reason: "A is on the angle bisector of PQR."

When a point lies on the angle bisector of an angle, it is equidistant from the two sides of that angle. The angle bisector theorem supports this statement as it indicates that the point on the bisector relates to two equal angles created by the bisector meeting the angle's sides.

This is a basic property of angle bisectors in geometry and can be proven using geometric constructions and congruent triangles.

The correct option is d.