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Given: Circle MGiven: Segment MA bisects Segment BCProve ?

a. Angle A is congruent to angle B.
b. Angle A is congruent to angle C.
c. Angle B is congruent to angle MAC
d. Angle B is congruent to Angle C

1 Answer

1 vote

Final answer:

In a circle with a bisecting segment MA, we can prove that angle A is congruent to angle B, angle A is congruent to angle C, angle B is congruent to angle MAC, and angle B is congruent to angle C. Therefore, the correct option is d).

Step-by-step explanation:

In the given scenario, we have a circle M, and segment MA bisects segment BC. We need to prove certain congruencies between angles.

a. To prove Angle A is congruent to angle B, we can use the fact that segment MA bisects segment BC. This means that segment BA is equal in length to segment AC.

As a result, angle B is congruent to angle C (by the Isosceles Triangle Theorem).

Since angle A and angle C are opposite angles in a parallelogram (formed by extending segment MA and segment BC), angle A is congruent to angle B.

b. To prove Angle A is congruent to angle C, we can use the same reasoning as in part a.

Since angle B and angle C are congruent (proved in part a), and angle A and angle B are congruent (proved by the transitive property of congruence), angle A is also congruent to angle C.

c. To prove Angle B is congruent to angle MAC, we can use the Angle Bisector Theorem.

Since segment MA bisects segment BC, it divides angle MAC into two congruent angles. Therefore, angle B is congruent to angle MAC.

d. To prove Angle B is congruent to Angle C, we can again use the transitive property of congruence.

Angle B is congruent to angle MAC (proved in part c), and angle MAC is congruent to angle C (proved in part a).

Therefore, angle B is congruent to angle C. Therefore, the correct option is d).

User Erben Mo
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