6. Isosceles and Equilateral Triangles
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Consider the Converse of the Isosceles Triangle Theorem.
FH=12
Consider the given triangle.
Classification of Triangles | |
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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 2π. |
Obtuse Triangle | An obtuse triangle is a triangle with exactly one an angle whose measure is greater than 90∘ or 2π. |
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.