3-5 Proving Lines Parallel
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Transcript 3-5 Proving Lines Parallel
Ms. Andrejko
Real World
Postulates and Theorems
Postulates
3.4
3.5
Theorems
3.5
3.6
3.7
3.8
Examples
Given the following information, determine which lines, if any,
are parallel. State the postulate or theorem that justifies your
answer
1. ∠3 ≅ ∠7
2. ∠9 ≅ ∠11
3. ∠2 ≅ ∠16
4. m∠5 + m∠12 = 180
Practice
Given the following information, determine which lines, if any,
are parallel. State the postulate or theorem that justifies your
answer.
1. m∠BCG + m∠FGC = 180
2. ∠CBF≅∠GFH
3. ∠EFB ≅∠FBC
4. ∠ACD ≅∠KBF
Examples
Find x so that ℓ // m .
Practice
Find x so that ℓ // m .
Examples
Given: <1 and <2 are complementary, BCCD
Prove: BA // CD
STATEMENTS
REASONS
BCCD
Given
<ABC= <1+<2
Angle Addition Post.
<1 and <2 are complementary Given
<1+<2 = 90
<ABC = 90
BABC
BA // CD
Def. of Complementary
Transitive
Def. of Perpendicular
Perp. Transversal Converse
Practice
Given: <2 and <3 are supplementary
Prove: AB // CD
STATEMENTS
1. <2&<3 are supplementary
<2 and <3 are
consecutive
AB // CD
REASONS
Given
2. Consecutive Interior
Angles Theorem
3. Consecutive Interior
Angles Converse