McGraw Hill Glencoe Geometry, 2012
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McGraw Hill Glencoe Geometry, 2012 View details
6. Isosceles and Equilateral Triangles
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Exercise 3 Page 289

Practice makes perfect

Consider the given triangle.

Looking at the labels on the given figure, we can see that We can write this by using a congruence statement.
Now, let's 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 or
Obtuse Triangle An obtuse triangle is a triangle with exactly one an angle whose measure is greater than or
Right Triangle A right triangle is a specific type of triangle that contains one angle of

Since the given triangle have two congruent angles, triangle is an isosceles triangle. We want to find To do so, we will use the Converse of the Isosceles Triangle Theorem.

Converse of the Isosceles Triangle Theorem

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

Using this theorem, let's show the congruent sides.

As a result, Therefore,