Transcript Lesson 3.2

Bell Ringer #
3-2 Proving Lines
Parallel
Postulate 3-2 Converse of the
Corresponding Angles Postulate
• If two lines and a transversal form
corresponding angles that are congruent, then
the two lines are parallel.
1
m‖ n
m
n
2
Theorems
• 3-3 Converse of the Alternate Interior Angles Thm
▫ If two lines and a transversal form alternate interior
angles that are congruent, then the lines are parallel.
3-4 Converse of the Same-Side Interior Angles Thm.
 If two lines and a transversal form same-side interior
angles that are supplementary, then the lines are parallel
• If ∠1 ≅ ∠2, then m ‖ n
• If ∠2 and ∠4 are
supplementary, then
m‖ n
m
4
1
2
n
Flow Proof
• Arrows show the logical connections between
the statements.
• Proving theorem 3-3
3
• Given: ∠1 ≅ ∠2
m
• Prove: m‖n
2
1
n
Theorems
• 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
t
b
c
m
n
Examples
• 1. which lines must be parallel if ∠1 ≅ ∠2? Justify
using a theorem or postulate.
3
E
D 1
C
4 K
2
• 3. Use algebra to find the value of x.
40°
(2x + 6)°
• 4. Find the value of x.
(7x – 8)°
62°
Ticket Out The Door
Practice
• Pg 125-126
• 1-3, 18 -20, and 27 - 30