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6.6 Proving Lines are Parallel (Due 4/9/2024)

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21 questions
Note from the author:
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Essential Question: How can you prove that two lines are parallel?

Learning Target: Students will be able to prove lines are parallel by analyzing and comparing the angles formed by a transversal.

Comlete the entire assignment and show all work for credit.
Essential Question: How can you prove that two lines are parallel?

Learning Target: Students will be able to prove lines are parallel by analyzing and comparing the angles formed by a transversal.

Comlete the entire assignment and show all work for credit.

Angles Formed by Parallels Cut by a Transversal

Key points about parallel lines cut by a transversal (These are your reasons):

Alternate Interior Angles are congruent


Alternate Exterior Angles are congruent


Corresponding Angles are congruent


Same-Side Interior Angles are supplementary


Same-Side Exterior Angles are supplementary



Also
Linear pairs of angles are supplementary


Vertical angles are congruent

Question 1
1.

Question 2
2.
Given the following information, a||b and c||d and ∠2 = 67°.

∠4= _______ What is the reason? _______
∠3= _______ What is the reason? _______
Question 3
3.

Match the example to what type of angle pair it represents.

Question 4
4.

In the figure below, line  n  is a transversal cutting lines  l  and  m.

Name the angle that is the alternate interior pair to ∠3.

Question 5
5.

In the figure below, line  n  is a transversal cutting lines  l  and  m.

Name the angle that is the same-side interior pair to ∠6.

Question 6
6.

In the figure below, line  n  is a transversal cutting lines  l  and  m.

Name the angle that is the same-side exterior pair to ∠1.

Question 7
7.

In the figure below, line  n  is a transversal cutting lines  l  and  m.

Name the angle that is the corresponding to ∠4.

Question 8
8.

In the figure below, line  n  is a transversal cutting lines  l  and  m. Line m || Line l

Name all the angles that are congruent to ∠4 not including ∠4.

Question 9
9.

In the figure below, line  n  is a transversal cutting lines  l  and  m. Line m || Line l

Name all the angles that are congruent to ∠3 not including ∠3.

Question 10
10.

In the figure below, line  n  is a transversal cutting lines  l  and  m. Line m || Line l

Name all the angles that are supplemental to ∠3.

Question 11
11.

In the figure below, line L₁, line L₂, line L₃, and line L₄, are parallel.

Name all the angles that are supplemental to ∠a.

Question 12
12.

In the figure below, line L₁, line L₂, line L₃, and line L₄, are parallel.

Name all the angles that are congruent to ∠e.

Question 13
13.
Find x so given that a || b.

x=_______

What is the reason?
_______
Question 14
14.
Find x so given that a || b.

x=_______

What is the reason?
_______
Question 15
15.
Find x so given that a || b.

x=_______

What is the reason?
_______
Question 16
16.
Find x so given that a || b.

x=_______

What is the reason?
_______
Question 17
17.
Find x so given that a || b.
x=_______

What is the reason?
_______
Question 18
18.
Find x so given that a || b.
x=_______

What is the reason?
_______
Question 19
19.
Find x so given that a || b.
x=_______

What is the reason?
_______
Question 20
20.
Find x so given that a || b.
x=_______

What is the reason?
_______
Question 21
21.
Find x so given that a || b.
x=_______

What is the reason?
_______
Match the angle pairs with their relationship.
equal 180 together
are the same size
Item 2
Item 1
Corresponding Angles
Alternate Interior Angles
Alternate Exterior Angles
Same-Side Interior Angles
Same-Side Exterior Angles