Question

question 16 of 20
which of the following are reasons used in the proof that the angle bisector construction can be used to bisect any angle?
check all that apply.
a. all of the radii of a circle are congruent.
b. sss triangle congruence postulate
c. cpctc
d. any line segment can be extended indefinitely

Explanation:

• Option A: In angle - bisector construction, we draw circles (arcs) with the vertex as the center. The radii of these circles (arcs) are used, and since all radii of a circle are congruent, this is a valid reason.
• Option B: When we construct the angle bisector, we create two triangles. By using the fact that radii are congruent and the common side, we can apply the SSS (Side - Side - Side) triangle congruence postulate to show the triangles are congruent.
• Option C: After proving the triangles congruent using SSS, we use CPCTC (Corresponding Parts of Congruent Triangles are Congruent) to show that the angles formed by the bisector are equal, so this is a valid reason.
• Option D: The angle - bisector construction does not rely on extending a line segment infinitely. So this is not a reason for the angle - bisector construction.

Answer:

A. All of the radii of a circle are congruent.
B. SSS triangle congruence postulate
C. CPCTC