Transcript 3.2 Angles Formed by Parallel Lines and Transversals

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2. Take out a protractor
3. Start working on the back of your notes from
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3.2: Angles Formed by Parallel
Lines and Transversals
Learning Objective :
 SWBAT prove and use theorems about the angles
formed by parallel lines and a transversal.
Whiteboards: Review
Identify each of the following.
1. a pair of parallel segments
EH || FG
2. a pair of skew segments
BF and EH
3. a pair of perpendicular segments
CG  GH
4. a pair of parallel planes
plane ABC and plane EFG
Whiteboards
Identify each angle pair.
1. 1 and 3
2. 3 and 6
3. 4 and 5
4. 6 and 7
3.2 Angles Formed by Parallel Lines
and Transversals
What would you call two lines that are on the same plane bdo not
intersect?
Exterior
B
A
Interior
D
C
Exterior
• A solid arrow placed on
two lines of a diagram
indicate the lines are
parallel.
• The symbol || is used to
indicate parallel lines.
• AB || CD
3.2 Angles Formed by Parallel Lines
and Transversals
A slash through the parallel symbol || indicates the
lines are not parallel.
AB || CD
B
A
D
C
3.2 Angles Formed by Parallel Lines
and Transversals
Special Angle Relationships WHEN THE LINES
ARE PARALLEL
♥Alternate Interior Angles
Exterior
are CONGRUENT
1
3 4
Interior
5 6
7 8
Exterior
2
♥Alternate Exterior Angles are
CONGRUENT
♥Same Side Interior Angles are
SUPPLEMENTARY
♥Same Side Exterior Angles are
SUPPLEMENTARY
3.2 Angles Formed by Parallel Lines
and Transversals
Example 1
Find mQRS.
3.2 Angles Formed by Parallel Lines
and Transversals
Example 2
Find each angle measure.
a. mECF
b. mDCE
3.2 Angles Formed by Parallel Lines
and Transversals
Example 3
Find the measure of each angle.
a. mEDG
b. mBDG
Example 4
Find mABD.
2x + 10° = 3x – 15°
x = 25
mABD = 2(25) + 10 = 60°
Alt. Int. s Thm.
Subtract 2x and add 15 to both sides.
Substitute 25 for x.
Example 5:
Find x and y in the diagram.
By the Alternate Interior Angles
Theorem, (5x + 4y)° = 55°.
By the Corresponding Angles Postulate, (5x +
5y)° = 60°.
5x + 5y = 60
–(5x + 4y = 55)
y=5
5x + 5(5) = 60
x = 7, y = 5
Subtract the first equation from the second
equation.
Substitute 5 for y in 5x + 5y = 60. Simplify and
solve for x.
Whiteboards
State the theorem or postulate that is related to the measures of
the angles in each pair. Then find the unknown angle measures.
1. m1 = 120°, m2 = (60x)°
Alt. Ext. s Thm.; m2 = 120°
2. m2 = (75x – 30)°,
m3 = (30x + 60)°
Corr. s Post.; m2 = 120°, m3 = 120°
3. m3 = (50x + 20)°, m4= (100x – 80)°
Alt. Int. s Thm.; m3 = 120°, m4 =120°
4. m3 = (45x + 30)°, m5 = (25x + 10)°
Same-Side Int. s Thm.; m3 = 120°, m5 =60°
Lesson Overview
Standards: A.CED.3
MP: 1,2,3,4,5
Vocabulary: Transversal, ….
Essential Question:
Learning Objective: Prove and use theorems about the angles
formed by parallel lines and a transversal.
Independent Practice: Pg. 148 #6-13, 26-29, 34, 42