Question

Harry completed the steps shown to construct an acute triangle. Points P and R represent two vertices of the triangle.


which point could represent the third vertex of the acute triangle?

A. Point N, because it lies beyond the arc.
B. Point O, because it lies on the perpendicular line.
C. Point L, because the measure of angle LPR is less than 90 degrees.
D. Point M, because the measure of angle MPR is greater than 90 degrees.

Answer 1

C. Point L, because the measure of angle LPR is less than 90 degrees.
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An acute triangle has alll three interior angles of measure less than 90. That is at the core of solving this problem.

The choice of any third vertex for the to be constructed acute triangle cannot be N or M because it would cause the triangle to be obtuse. The third vertex cannot be O because it would cause the triangle to be right.

That leaves L as the third vertex. The angle it forms is contained within a right angle making its measure less than 90.

Answer 2

okay , thanks ! Now i actually understand now ! thanks so much!

Answer 3

Glad to help.