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 48 Page 381

Find m∠ G by considering the Isosceles Triangle Theorem and the Triangle Sum Theorem.

Both are incorrect. See solution.

Practice makes perfect

Alexis and Miguela are finding m∠ G in the figure shown.

We want to see whether either of them is correct. To do so, we will start by recalling 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^(∘).

The given triangle has two congruent sides, which means that it is an isosceles triangle. Because of this, we can use the Isosceles Triangle Theorem to find m∠ G.

Isosceles Triangle Theorem

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

This means that m∠ G=m∠ H. We can use this information and the Triangle Sum Theorem to find the measure of ∠ G.
m∠ G+m∠ H+ m∠ F=180
m∠ G+ m∠ G+ 70 =180
2m∠ G+ 70 =180
2m∠ G=110
m∠ G=55
Since m∠ G is 55, neither is correct.