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.