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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

4. Equilateral and Isosceles Triangles

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Exercise 16 Page 612

Start by identifying congruent sides.

$x = 7$
$y = 4$

Practice makes perfect

Let's start with the isosceles triangle. According to the Converse of the Base Angles Theorem, if two angles of a triangle are congruent, then the sides opposite them are congruent.

Let's now turn to the equiangular triangle. According to the Corollary to the Converse of the Base Angles Theorem, if a triangle is equiangular, then it is equilateral. We will add this information as well to the diagram.

All of the marked sides are congruent. Using this fact, we can write an equation that only contains

y .

5 y - 4 = y + 12

Let's solve this equation.

5 y - 4 = y + 12

▼

Solve for

y

$LHS - y = RHS - y$

4 y - 4 = 12

$LHS + 4 = RHS + 4$

4 y = 16

$LHS / 4 = RHS / 4$

y = 4

When we know that

y = 4,

we can calculate two of the sides:

y + 12 : 5 y - 4 : 4 + 12 = 16 5 (4) - 4 = 16

The congruent sides have a length of

16 .

Now we have enough information to solve for the last side as well.

3 x - 5 = 16

$LHS + 5 = RHS + 5$

3 x = 21

$LHS / 2 = RHS / 2$

x = 7

Subchapter links

Communicate Your Answer p.607

Monitoring Progress p.609-611

Exercises p.612-614