McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
5. Isosceles and Equilateral Triangles
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Exercise 41 Page 381

m∠ LMP=80

Practice makes perfect

Looking at the given diagram, we see that LM≅ LP.

Now, we will recall the classification of triangles.
Classification of Triangles
Scalene Triangle A scalene triangle is a triangle in which all three sides have different lengths.
Isosceles Triangle An isosceles triangle is a triangle that has two congruent sides and two base angles with the same measure.
Equilateral Triangle An equilateral triangle is a triangle in which all the sides are congruent.
Acute Triangle An acute triangle is a triangle where all angles are less than 90^(∘) or π2.
Obtuse Triangle An obtuse triangle is a triangle with exactly one an angle whose measure is greater than 90^(∘) or π2.
Right Triangle A right triangle is a specific type of triangle that contains one angle of 90^(∘).

Since the given triangle has two congruent sides, triangle LMP is an isosceles triangle. We want to find m ∠ LMP. To do so, we will consider the Isosceles Triangle Theorem.

Isosceles Triangle Theorem

If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

This means that m∠ LMP=m∠ LPM. Since we have found the measure of ∠ LPM as 80^(∘) in the previous exercise, we can determine immediately that m∠ LMP.
m∠ LMP=m∠ LPM
m∠ LMP=80
As such, the measure of ∠ LMP is 80^(∘).