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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,螖ABC is equilateral such that AB炉鈮�BC炉鈮�CA炉.

Statements

Reasons

1.AB炉鈮�AC炉

From the figure

2.鈭�B鈮�鈭�C

Isosceles theorem

3.AB炉鈮�BC炉

From the figure

4.鈭�C鈮�鈭�A

Isosceles theorem

5.CA炉鈮�BC炉

From the figure

6.鈭�A鈮�鈭�B

Isosceles theorem

7.鈭�A鈮�鈭�B鈮�鈭�C

Transitive property

8.螖ABC 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 螖ABC. If so, write the congruence and name the postulate used. If not, write no congruence can be deduced.

Can two triangles be proved congruent? If so, by which method, SSS, SAS, ASA, AAS, or HL?

Yes, the two triangles can be proved congruent 螖ABC鈮�螖DEC, by HL method.

Given: 鈭�S鈮�鈭�T;ST炉||QP炉

Which one(s) of the following must be true?

(1)鈭�P鈮�鈭�Q

(2)PR炉鈮�QR炉

(3) R is the midpoint of PT炉

State whether the congruence of triangles have the reflexive property, the symmetric property, the transitive property.

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b. The town also wants to build a boat-launching site that is equidistant from Elm Road and Main Street. Find the point L where it should be built.

c. On your diagram, locate the spot Ffor a flagpole that is to be the same distance from the recreation center, the school, and the courthouse.
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