Exercise 4 Page 378

Consider the Properties of Equilateral Triangles.

m ∠ MRP= 60

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Consider the given triangle.

The red lines over the sides of the triangle mean that all the sides have the same size and shape. This means that all the sides are congruent. We can write this by using a congruence statement. PM≅MR≅RP Now, 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.
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 three congruent sides, triangle MPR is an equilateral triangle. We want to find m ∠ MRP. To do so, we will consider the Properties of Equilateral Triangles.

A triangle is equilateral if and only if it is equiangular.
Each angle of an equilateral triangle measures 60^(∘).

Using the second property, we can say that m ∠ MRP= 60.

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