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 3 Page 378

FH=12

Practice makes perfect

Consider the given triangle.

Looking at the labels on the given figure, we can see that m ∠ GFH = m ∠ HGF. We can write this by using a congruence statement.

∠ GFH ≅ ∠ HGF 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 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 have two congruent angles, triangle FGH is an isosceles triangle. We want to find FH. 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, GH≅ FH. Therefore, FH=12.