# 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
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
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: &lt;1 and &lt;2 are complementary, BC  CD
 Prove: BA // CD
STATEMENTS
REASONS
BC  CD
Given

&lt;ABC= &lt;1+&lt;2
&lt;1 and &lt;2 are complementary Given
&lt;1+&lt;2 = 90
&lt;ABC = 90
BA  BC
BA // CD
Def. of Complementary
Transitive
Def. of Perpendicular
Perp. Transversal Converse
Practice
 Given: &lt;2 and &lt;3 are supplementary
 Prove: AB // CD
STATEMENTS
1. &lt;2&amp;&lt;3 are supplementary
&lt;2 and &lt;3 are
consecutive
AB // CD
REASONS
Given
2. Consecutive Interior
Angles Theorem
3. Consecutive Interior
Angles Converse
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