Q12. Explain how corollary follows fr... [FREE SOLUTION]

91影视

Geometry

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: Q12. (page 136)

Explain how corollary follows from theorem 4-2.

Short Answer

Expert verified

An equilateral triangle is also equiangular the two angles are congruent, then the sides opposite to those angles are congruent.

Step by step solution

Step 1. Consider the figure.

Consider the figure.

Step 2. Apply the concept of isosceles triangles.

Equiangular: When all the interior angles are equal in measure or say all angles are congruent, then the figure is said to be equiangular.

The Isosceles Triangle Theorem: If Two angles are congruent, then the sides opposite to those angles are congruent. Corollary 1: An equilateral triangle is also equiangular.

Theorem 4-2, Two angles are congruent, then the sides opposite to those angles are congruent

Step 3. Step description.

Use the two-column form as follows:

Statements	Reasons
1. $螖 A B C$ is equiangular	From the statement
2. $鈭� A 鈮� 鈭� C$	Definition of equiangular triangle
3. $\overset{炉}{A B} 鈮� \overset{炉}{B C}$	Converse of isosceles theorem
4. $鈭� B 鈮� 鈭� C$	Definition of equiangular triangle
5. $\overset{炉}{A B} 鈮� \overset{炉}{A C}$	Converse of isosceles theorem
6. $鈭� A 鈮� 鈭� B$	Definition of equiangular triangle
7. $\overset{炉}{B C} 鈮� \overset{炉}{A C}$	Converse of isosceles theorem
8. $\overset{炉}{A B} 鈮� \overset{炉}{B C} 鈮� \overset{炉}{A C}$	Transitive property
9. $螖 A B C$ is equilateral	Definition of equilateral