Question

In Exercises 1-3, the perpendicular blsectors of ABC Intersect at point G, or the anglebisectors of AXYZ intersect at point P. Find the Indicated measure. Tell which theoremyou used.

Answer 1

Perpendicular bisectors

Initial explanation

We have a line:

And we draw its perpendicular bisector:

Then, any point on the bisector is equidistant to the endpoints of the line:

This is called: the perpendicular bisector theorem.

1

In this case we have that:

Since the line is the black one, the bisector is the purple one, then both red segments measure the same : 9.

Answer: BG = 9 (bisector theorem)

2

In this case, as we can observe in the image, the red lines are equidistant then CG = 10

Answer: CG = 10 (bisector theorem)