For the following:
a. Draw a diagram
b. Write a conclusion that states the congruence of the two angles.
c. Write a conclusion that states the equality of the measures of two angles.
14. CD bisects angle ACB. (CD is a ray)
Thanks
Which statement is true?
Select one of the options below as your answer:
A.
Two angles can be complementary and equal.
B.
Two angles cannot be equal if they are complementary.
C.
An angle can be complementary only if it is 90°.
D.
Only three angles can be supplementary.
To answer the given question, we need to draw a diagram and use the properties of angle bisectors.
a. Drawing a diagram:
To draw the diagram, we can start by drawing line AB with a point C on it. Then, draw a ray CD starting from point C, such that it intersects the angle ACB. The ray CD should divide the angle ACB into two equal angles, ∠ACD and ∠DCB.
Here is a diagram:
A
|\
| \
∠ACD | \ ∠DCB
| \
C----D
|
B
b. Writing a conclusion that states the congruence of the two angles:
Since CD is an angle bisector, it divides angle ACB into two congruent angles, ∠ACD and ∠DCB. Therefore, we can conclude that ∠ACD ≅ ∠DCB.
c. Writing a conclusion that states the equality of the measures of two angles:
By the definition of angle bisector, CD divides angle ACB into two equal angles. This means that the measures of ∠ACD and ∠DCB are equal, ∠ACD = ∠DCB.