Question

The figure below shows the incenter, D, of the triangle ABC.

Triangle ABC is drawn. Two segments; CD bisects angle ACB is drawn, and BD bisects angle ABC is drawn

Which statement is always correct about the triangle ABC?

Measure of angle ABD is equal to measure of angle BAC.

Segment AD is congruent to segment DE.

Segment DC is congruent to segment DB.

Measure of angle ACD is equal to measure of angle DCB.

Answer 1

Is it Segment DC is congruent to segment DB.?

Answer 2

Where is the figure below?

>>The figure below shows the incenter, D,

Answer 3

>Is it Segment DC is congruent to segment DB.?

No, just a sec. I need to draw something.

Answer 4

> CD bisects angle ACB is drawn,

What does it mean about the two angles that form angle ACB if segment CD bisects angle ACB?

Answer 5

Which option goes with the figure I drew?

The point D is the incenter which is the point of concurrency (common intersection) of all 3 angle bisectors of the triangle but that the incenter "stuff" doesn't figure into this because this information was given: Two segments; CD bisects angle ACB is drawn, and BD bisects angle ABC is drawn.

Answer 6

If CD *bisects* angle ACB, then what is true about the two angles <ACD and <DCB with regard to their measures.

Answer 7

@Ashja

Answer 8

Measure of angle ACD is equal to measure of angle DCB.

Answer 9

That is what I got, the last option.

Answer 10

Thanks for explaining everything!

Answer 11

Happy to help.