Question

The figure below shows the incenter, N, of the triangle KLM.

Triangle KLM is drawn. The incenter of the triangle is labeled as point N. Segments KN and NL are drawn. A segment MP passes through point N and intersects KL at point P.

Which statement is always true?

The segment MN is congruent to the segment NP.

The segment KN is congruent to the segment LN.

Angle MKN is congruent to angle LKN.

Angle MKN is congruent to angle NLM.

Answer 1

Hint:

The angle bisectors of any triangle always intersect at the incenter

Answer 2

so its either c or d ?

Answer 3

good, so which one are you thinking?

Answer 4

an angle bisector, turns one angle into two equal angles

ie it cuts the angle into two equal halves

Answer 5

Visually you go from this

Answer 6

to this

Answer 7

segment BD cuts angle ABC into two equal halves

those two smaller (and congruent) angles are: ABD and DBC

Answer 8

im guessing D

Answer 9

here is angle MKN

Answer 10

it's marked in red

Answer 11

yeahh i see it so would it be c then

Answer 12

and angle NLM is the angle marked in blue

Answer 13

are those two angles congruent?

Answer 14

it doesnt look lke it

Answer 15

they could be, but there are no guarantees

Answer 16

so D is not always true, so that's why we can eliminate it

but C is correct because these two angles are congruent (marked in red and blue) because the angle bisector always cuts the angle into two equal halves

Answer 17

the red angle is MKN and the blue angle is LKN

Answer 18

in that last pic I posted

Answer 19

thanks for the explanation

Answer 20

yw