Download LP-Investigation Parallel and Transversal

Topic: Angle
Relationship
Parallel cut by
transversal
Materials:
Co-teaching Model :
Protractor, IP worksheet
Thursday:
Teacher will be circulating as
facilitator
Friday:
Lesson 4 will break into small
groups of 4
Groupings:
Pair of 2
Small groups Friday
Date:
Two days Lesson
Exploration 4/3/12
and Application 4/4/12
Do now
Direct Instruction
Content Objective:
Students will be able to identify
angle relationship such alternate
exterior angle, alternate interior
angle, corresponding angles,
vertical and supplemental angles
Re-Teach Do now
Lesson 3
Have students fold a 8.5 x 11 sheet of paper into thirds “hot-dog” style.
Using a ruler, have students use a thick marker and trace the folded line.
Have students draw a transversal, making sure that all students draw the
transversal in the same direction you do (model this on the board). Then,
have students label each angle with a number 1 – 8. Make sure that all
students label the angles in the same order you do (model this on the
board). Also, make sure students have marked the angles with an arc. Then
have students use scissors and cut along the lines made by the markers.
Have students separate the angles into piles of congruent angles. Ask
students:
 How many angles are in each pile?
 How are the angles in each pile similar?
 How are the angles in each pile different?
 What are the similarities and differences between both piles?
 How many different angle measures are there total?
Have students mark each pile of angles with the same symbol (perhaps 4
happy faces for one pile, and 4 stars for the other pile)
Have students reassemble the angles until they’re back where they started
(like a puzzle). Ask students:
 Do you notice any patterns about where the angles from each pile
are now positioned?
 Which angles are the same?
 Which ones are different?
 Which ones are acute?
 Which ones are obtuse?
 What is the angle relationship between the two different angles
(one acute and one obtuse)?
Guided Practice
When two parallel lines are cut by a third line, called the transversal, some
special angle relationships are formed.
From our exploration we know that…
<1 @ < 4, 5, Ð 8
Ð 2 @ Ð 3, Ð 6, Ð 7
Ð 5 @ Ð 8, Ð 1, Ð 4
Ð 6 @ Ð 7, Ð 3, Ð 2
Ð 1 + Ð 2 = 180 degrees
Ð 1 + Ð 3 = 180 degrees
Feel free to test other combinations here, such as Ð 1 and Ð 7
How many other angles are supplementary to Ð 1? 4 angles ( Ð 2, Ð 3, Ð
6, Ð 7)
How many other angles are congruent to Ð 1? 3 angles, total of 4
Corresponding Angles (When you slide ‘em, they take the same spot!)
Since corresponding angles are the same shape and same size, we know
they are congruent. That means their angle measures are equal (the same).
Ð 1 corresponds to Ð 5
Ð 2 corresponds to Ð 6
Ð 3 corresponds to Ð 7
Ð 4 corresponds to Ð 8
Ð 5 corresponds to Ð 1
Ð 6 corresponds to Ð 2
Ð 7 corresponds to Ð 3
Ð 8 corresponds to Ð 4
Alternate Interior Angles (A.I.A.)
Alternate Interior Angles are congruent
“Alternate” refers to the angles being on opposite sides of the transversal.
“Interior” refers to the angles being on the inside of the parallel lines.
Have students derive a three-step or two-step proof proving that angle A is
congruent to angle G.
Example 1:
Angle A is supplementary to angle B
Angle B corresponds to angle F
Angle F is supplementary to angle G
So, Angle A is congruent to Angle G
Example 2:
Angle A corresponds to Angle E
Angle E and Angle G are vertical angles
So, Angle A is congruent to Angle G
So, we can conclude that if two angles are alternate interior angles, their
measures are the same.
Alternate Exterior Angles (A.E.A.)
Alternate Exterior Angles are congruent.
“Alternate” refers to the angles being on opposite sides of the transversal.
“Exterior” refers to the angles being on the outside of the parallel lines.
Have students derive a three-step or two-step proof proving that angle C is
congruent to angle E.
Example 1:
Angle C is supplementary to angle D
Angle D corresponds to angle H
Angle H is supplementary to angle E
So, Angle C is congruent to Angle E
Example 2:
Angle C corresponds to Angle G
Angle G and Angle E are vertical angles
So, Angle C is congruent to Angle E
Independent Practice
Lesson 4
Part 2: Finding the missing angles Application
Example 1: Find Angle Measures of Parallel Lines Cut by Transversals
1. Work through each question.
2. Have students first identify the angle relationship and tell you
what they know about the relationship
3. Then have students explain how they found the angle measure
4. Have students say why their answer makes sense (the angle is
acute, and it’s also an acute angle so I know they are the same
because in this diagram all the acute angles are congruent).
5. Work through You Try 1.
How many different angles would be formed by a transversal intersecting
three parallel lines? How many different angle measures would there be?
(encourage students to draw a picture)
Explain how a transversal could intersect two other lines so that
corresponding angles are not congruent. (transversals going in different
directions)
Can you think of two real-world examples of parallel lines? How are these
examples different from the mathematical concept of parallel lines? (streets
in Boston, train tracks, etc.)
Assessment/Reflection:
Exit Ticket : lesson 3 and lesson 4
Homework
Accommodations:
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