Exercise 41 Page 381

Consider the Isosceles Triangle Theorem.

m∠ LMP=80

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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

Substitute

m∠ LPM= 80

m∠ LMP=80

As such, the measure of ∠ LMP is 80^(∘).

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