In △MNP , point Q is between points M and N, and point R is between points N and P. Point H is the incenter of the triangle, HQ⊥MN, and HR ⊥NP. QN=36 and HN=39 . What is HR ? Enter your answer in the box.

15

Step-by-step explanation:

The given parameters are represented by drawing the triangle with the details given using MS Visio

The point Q is located between points M and N in ΔMNP

The point R is located between points N and P in ΔMNP

The incenter of the triangle = H

Line HQ is perpendicular to side MN on ΔMNP

Line HR is perpendicular to side NP on ΔMNP

The length of the segment QN = 36

The length of the segment HN = 39

By Pythagoras' theorem, HQ = √((HN)² - (QN)²)

∴ HQ = √(39² - 36²)  = 15

HQ = 15

Given that H is the incenter of ΔMNP, the lengths of the perpendicular from H to the sides of the triangle are equal to the radius of the inscribed circle of the triangle

Therefore, the radius lengths are HQ, and HR

∴ HR = HQ = 15

HR = 15.

parallel and congruent

step-by-step explanation:

the movement of translation is linear.   these have the same translation because you are using the same rule for each point of the triangle so you will see the same slope being used to get from a point on the triangle to its image.

same slope!   you should think parallel when you see those 2 word together (well unless it's the same line but it can't be because we are coming from different points here)

congruent! because each point is being moved the same distance.