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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

3. Proofs with Parallel Lines

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Exercise 8 Page 514

Use the Converse of the Alternate Interior Angles Theorem.

$x = 20$

Practice makes perfect

Both angles are in the interior of the diagram and on opposite sides of the transversal. Therefore, they are alternate interior angles.

According to the Converse of the Alternate Interior Angles Theorem, if the angles are congruent, then the lines are parallel.

2 x + 20 = 3 x

Let's solve this equation.

2 x + 20 = 3 x

$LHS - 2 x = RHS - 2 x$

20 = x

Rearrange equation

x = 20

When

x = 20,

the lines

m

and

n

are parallel.

Subchapter links

Communicate Your Answer p.509

Monitoring Progress p.510-513

Exercises p.514-516