Proving Lines Parallel

Check Skills You’ll NeedSolve each equation.

1. 2x + 5 = 272. 8a – 12 = 203. x – 30 + 4x + 80 = 1804. 9x – 7 = 3 x + 29

Write down the converse of each conditional statement. Determine the truth value of the converse.

5. If a triangle is a right triangle, then it has a 90 degree angle.6. If two angles are vertical angels, then they are congruent.7. If two angles are same-side interior angles, then they are supplementary.

Postulate 3-2If two lines and a transversal form corresponding angles that are congruent, then the two lines are parallel.

1

2

l

m

Theorem 3 – 3 Converse of the Alternate Interior Angles Theorem

If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel.

If /_ 1 = /_ 2, then l ll m

1

2

l

m4

Theorem 3 – 4If two lines and a transversal for same-side interior angles that are supplementary, then two lines are parallel.

If /_ 2 and /_ 4 are supplementary, then l ll m

1

2

l

4

m

Proving Theorem 3-3

Given /_ 1 = /_ 2Prove: l || m

/_ 1 = /_ 2 Given/_ 1 = /_ 3 Vertical Angles/_ 2 = /_ 3 Transitive Propertyl || m Postulate 3-2

1

2

l3

m

Which lines, if any, must be parallel if ? Justify your answer with a theorem or postulate.

DE || KC by theorem 3-3, the converse of the alternate interior angles theorem: If alternate interior angles are congruent, then the lines are parallel.

D

E C

K12

3

4

Theorem 3-5If two lines are parallel to the same line, then they are parallel to

each other

Theorem 3-6 In a plane, if two lines are perpendicular to the same line, then

they are parallel to each other.

ab

c

m

t

n

Given: r t, s t Prove: r||t

m/_ 1 = 90; m/_ 2 = 90m/_ 1 = m/_ 2r||t

1 2

r s

t

Find the value of x for which l ll m

40

(2x + 6)

l

m