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Chapter 4: Q9. (page 136)

Explain how corollary 1 follows from theorem 4-1 such that an equilateral triangle is also equiangular.

Short Answer

Expert verified

An equilateral triangle is also equiangular.

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.

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 sides of a triangle are congruent, then the angles opposite to those sides are congruent.

03

Step 3. Step description.

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

Statements

Reasons

1.AB¯≅AC¯

From the figure

2.∠B≅∠C

Isosceles theorem

3.AB¯≅BC¯

From the figure

4.∠C≅∠A

Isosceles theorem

5.CA¯≅BC¯

From the figure

6.∠A≅∠B

Isosceles theorem

7.∠A≅∠B≅∠C

Transitive property

8.ΔABC is equiangular

Definition of equiangular

Thus, the above proof shows that how corollary 1 follows from the Isosceles triangle theorem.

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Most popular questions from this chapter

Decide whether you can deduce by the SSS, SAS, or ASA postulate that another triangle is congruent to ΔABC. If so, write the congruence and name the postulate used. If not, write no congruence can be deduced.

For the following figure, can the triangle be proved congruent? If so, what postulate can be used?

Find the values ofx and y.

27. ln equiangular ΔABC,AB=4x-y,BC=2x+3y and AC=7.

For the following figure, does the SAS postulates justify that the two triangles are congruent.

Decide whether you can deduce by the SSS, SAS, or ASA postulate that another triangle is congruent to ΔABC. If so, write the congruence and name the postulate used. If not, write no congruence can be deduced.
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