Pearson Geometry Common Core, 2011
PG
Pearson Geometry Common Core, 2011 View details
3. Bisectors in Triangles
Continue to next subchapter

Exercise 18 Page 305

Where do the angle bisectors intersect?

x=4

Practice makes perfect

Looking at the markings on the given diagram, we can see that MR bisects ∠ M and LR bisects ∠ L.

Therefore, we know that these segments are angle bisectors and that they intersect at the triangle's incenter. According to the Concurrency of Angle Bisectors Theorem, the incenter of a triangle is equidistant from the sides of the triangle. RS = RT Now that we know that these segments have equal lengths, we can equate the given expressions for RS and RT to solve for x.
RS=RT
4(x-3)+6= 5(2x-6)
Solve for x
4x-12+6 =5(2x-6)
4x-12+6=10x-30
4x-6=10x-30
4x+24=10x
24=6x
4=x
x=4