Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole

Chapter 3 - Section 3.3 - Isosceles Triangles - Exercises - Page 145: 20

Answer

(a) It is possible for a triangle to be an acute isosceles triangle. (b) It is possible for a triangle to be an obtuse isosceles triangle. (c) It is not possible for a triangle to be an equiangular isosceles triangle.

Work Step by Step

(a) It is possible for a triangle to be an acute isosceles triangle. One angle has a measure of $x$ where $0 \lt x \lt 90^{\circ}$ The two other angles measure $\frac{180^{\circ}-x}{2}$ (b) It is possible for a triangle to be an obtuse isosceles triangle. One angle has a measure of $x$ where $90^{\circ} \lt x \lt 180^{\circ}$ The two other angles measure $\frac{180^{\circ}-x}{2}$ (c) It is not possible for a triangle to be an equiangular isosceles triangle. If all three angles measure $60^{\circ}$, then the triangle is an equilateral triangle, not an isosceles triangle.

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