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Proving Lines Parallel

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Proving Lines Parallel

Solve each equation.

- 2x + 5 = 27
- 8a – 12 = 20
- x – 30 + 4x + 80 = 180
- 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 3-2

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

l

1

m

2

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 llm

l

1

4

m

2

Theorem 3 – 4

If 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 llm

l

1

4

m

2

Given /_ 1 = /_ 2

Prove: l ||m

/_ 1 = /_ 2 Given

/_ 1 = /_ 3 Vertical Angles

/_ 2 = /_ 3 Transitive Property

l ||m Postulate 3-2

l

3

1

m

2

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

3

E

C

4

D

1

K

2

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.

Theorem 3-5

If 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.

a

b

c

t

m

n

Given: r t, s t

Prove: r||t

m/_ 1 = 90; m/_ 2 = 90

m/_ 1 = m/_ 2

r||t

r

s

1

2

t

Find the value of x for which lllm

40

l

m

(2x + 6)