Q10. Explain how corollary 2 follows ... [FREE SOLUTION]

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 4: Q10. (page 136)

Explain how corollary 2 follows from corollary such that an equilateral has three 60-degree angles.

Expert verified

An equilateral triangle has three 60-degree angles.

Consider the figure of equilateral triangle.

Corollary 1: An equilateral triangle is also equiangular.

Corollary 2: An equilateral triangle has three 60-degree angles.

The Isosceles Triangle Theorem: If two sides of a triangle are congruent, then the angles opposite to those sides are congruent.

From the figure, $螖 A B C$ is equilateral such that $\overset{炉}{A B} 鈮� \overset{炉}{B C} 鈮� \overset{炉}{C A}$ .

Statements	Reasons
1. $\overset{炉}{A B} 鈮� \overset{炉}{A C}$	is equilateral
2. $鈭� A 鈮� 鈭� B 鈮� 鈭� C$	Corollary 1
3. $m 鈭� A = m 鈭� B = m 鈭� C$	Definition of congruent angles
4. $m 鈭� A = m 鈭� B = m 鈭� C = 180 掳$	Sum of angles of a triangle is
5. $m 鈭� A + m 鈭� A + m 鈭� A = 180 掳 3 脳 m 鈭� A = 180 掳 m 鈭� A = \frac{180 掳}{3} = 60 掳$	Substitution property
6. Similarly, $m 鈭� B = m 鈭� C = 60 掳$	From the previous step