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McGraw Hill Integrated II, 2012 View details

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Exercise 25 Page 396

Consider the properties of equiangular triangles.

x=3

Practice makes perfect

In the given figure, we see that interior angles of the triangle are congruent.

We know that a triangle with three congruent angles is equiangular. This means that the sides of the given triangle must also be congruent. Therefore, the side lengths are equal. We can use any two of the given expressions to set up and solve an equation for x. 7x-7=5x-1 Let's solve this equation for x!

7x-7=5x-1

AddEqn

LHS+7=RHS+7

7x=5x+6

SubEqn

LHS-5x=RHS-5x

2x=6

DivEqn

.LHS /2.=.RHS /2.

x=3

Checking Our Answer

Finding the side lengths

We can now substitute x=3 in the given expressions to get the side lengths of the triangle and check whether it is equilateral.

Expression	Substitution	Side Length
10/3x+4	10/3( 3)+4	14
5x-1	5( 3)-1	14
7x-7	7( 3)-7	14

Therefore, the side lengths are equal.

Subchapter links

1 Angles of Triangles p.394

2 Congruent Triangles p.394

3 Proving Triangles Congruent-SSS, SAS p.395

4 Proving Triangles Congruent-ASA, AAS p.395

5 Isosceles and Equilateral Triangles p.396

6 Triangles and Coordinate Proof p.396

Exercise 25 Page 396

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