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McGraw Hill Glencoe Geometry, 2012

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McGraw Hill Glencoe Geometry, 2012 View details

Study Guide and Review

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Exercise 31 Page 313

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 .

7 x - 7 = 5 x - 1

Let's solve this equation for

x!

7 x - 7 = 5 x - 1

$LHS + 7 = RHS + 7$

7 x = 5 x + 6

$LHS - 5 x = RHS - 5 x$

2 x = 6

$LHS / 2 = RHS / 2$

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
$\frac{1 0}{3} x + 4$	$\frac{1 0}{3} (3) + 4$	$14$
$5 x - 1$	$5 (3) - 1$	$14$
$7 x - 7$	$7 (3) - 7$	$14$

Therefore, the side lengths are equal.