Post on 17-Jan-2018
description
•Prove that 2 lines are parallel.•Use properties of parallel lines to solve problems.
3-4 Proving Lines are Parallel
Corresponding Angles Converse Postulate
•If 2 lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.
1
2
Theorem 3.8 (AIA Converse): If 2 lines are cut by a transversal so that AIA are congruent then the lines are parallel.
Proving AIA Converse
1
2
3Given: 1 2Prove: p q
1. 1 2 1. Given2. 1 33. 2 34. p q
2. Vert. ’s Theorem3. Trans. POC4. Corres. ’s Converse
p
q
Statements Reasons
Theorem 3.9 (CIA Converse): If 2 lines are cut by a transversal so that CIA are supplementary then the lines are parallel.
Proving CIA ConverseGiven: Angles 4 and 5 are supplementary.
Prove: p and q are parallel
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5
p
q
2. Linear Pair Postulate
1. 4 and 5 are supplementary. 1. Given
2. 5 and 6 are supplementary.
3. 4 6
4. p q
Statements Reasons
4. AIA Converse
3. Supplements Theorem
Identify the Parallel Rays
6258
5961
A B C D
E F
3-5 Using Properties of Parallel Lines
•Use properties of parallel lines in problem solving
•Construct parallel lines
Theorem 3.11: If 2 lines are parallel to the same line, they are parallel to each other
Given:Prove:
p q and q r p r
pq
r1
23
1. p q, q r2. 1 2
1. Given
3. 2 34. 1 35. p r
2. Corres. ’s Post. 3. Corres. ’s Post. 4. Trans. POC5. Corres. ’s Converse
Theorem 3.12: If 2 lines in the same plane are perpendicular to the same line, they are parallel to each other
Given:
Prove:
,m p n p m n
m n
p1 2
1. m p, n p2. 1 & 2 are right angles.
1. Given
3. m1 = m22. Def. of lines3. Right Theorem 4. 1 2 4. Def. of ’s
5. m n 5. Corres. ’s Converse