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Chapter 4: Q10. (page 136)

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

Short Answer

Expert verified

An equilateral triangle has three 60-degree angles.

Step by step solution

01

Step 1. Consider the figure.

Consider the figure of equilateral triangle.

02

Step 2. Apply the concept of isosceles triangles.

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.

03

Step 3. Step description.

From the figure, ΔABCis equilateral such that AB¯≅BC¯≅CA¯.

Statements

Reasons

1.AB¯≅AC¯

is equilateral

2.∠A≅∠B≅∠C

Corollary 1

3.m∠A=m∠B=m∠C

Definition of congruent angles

4.m∠A=m∠B=m∠C=180°

Sum of angles of a triangle is

5.m∠A+m∠A+m∠A=180°3×m∠A=180°m∠A=180°3=60°

Substitution property

6. Similarly,m∠B=m∠C=60°

From the previous step

Thus, the above proof above shows that how Corollary 2 follows from Corollary 1.

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