Unit 1B – Angles and Parallel Lines Notes
Name
Date
I can…
Essential Question(s):
Key Concepts
Notes
Postulate
Theorem
Corresponding Angles Postulate
If two parallel lines are cut by a transversal, then
each pair of corresponding angles is
________________________________________.
Alternate Interior Angles Theorem
If two parallel lines are cut by a transversal, then
each pair of alternate interior angles is
________________________________________.
Consecutive Interior Angles Theorem
If two parallel lines are cut by a transversal, then
each pair of consecutive interior angles is
________________________________________.
Alternate Exterior Angles Theorem
If two parallel lines are cut by a transversal, then
each pair of alternate exterior angles is
________________________________________.
Of our six angle relationships, classify each as either
supplementary or congruent.
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Congruent Angles
Supplementary Angles
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Key Concepts
Notes
Example 1 - Given: In the figure below, ∠1 = 90° .
Find the measure of each angle and give a justification.
𝑚∠1 = _______ because
𝑚∠7 = _______ because
𝑚∠2 = _______ because
𝑚∠8 = _______ because
𝑚∠3 = _______ because
𝑚∠9 = _______ because
𝑚∠4 = _______ because
𝑚∠10 = _______ because
𝑚∠5 = _______ because
𝑚∠11 = _______ because
𝑚∠6 = _______ because
𝑚∠12 = _______ because
Example 2 – Find Missing Angles
Given: In the figure, 𝑚∠3 = 85° and 𝑚∠12 = 55° . Find
the measure of each angle and give a justification.
because
𝑚∠7 = _______ because
𝑚∠8 = _______ because
𝑚∠9 = _______ because
𝑚∠10 = _______ because
𝑚∠1 = _______ because
𝑚∠11 = _______ because
𝑚∠2 = _______ because
𝑚∠12 = _______ because
𝑚∠3 = _______ because
𝑚∠13 = _______ because
𝑚∠4 = _______ because
𝑚∠14 = _______ because
𝑚∠5 = _______ because
𝑚∠15 = _______ because
𝑚∠6 = _______ because
𝑚∠16 = _______ because
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Angles formed by two parallel lines and a transversal can be used to find unknown values.
Example 1 – Find Values of Variables
If 𝑚∠1 = 3𝑥 + 40, 𝑚∠2 = 2(𝑦 − 10), 𝑎𝑛𝑑
𝑚∠3 = 2𝑥 + 70, 𝑓𝑖𝑛𝑑 𝑥 𝑎𝑛𝑑 𝑦
Setup
Rationale
Setup
Rationale
Setup
Rationale
X – Value
Y – Value
Example 2 – Find Values of Variables
𝐹𝑖𝑛𝑑 𝑥 𝑎𝑛𝑑 𝑦
X – Value
Y – Value
Example – Find Values of Variables
If 𝑚∠1 = 3𝑥 + 15, 𝑚∠2 = 4𝑥 − 5
𝑚∠3 = 5𝑦 𝑎𝑛𝑑 𝑓𝑖𝑛𝑑 𝑥 𝑎𝑛𝑑 𝑦
X – Value
Y – Value
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Unit 1B – Angles and Parallel Lines
Name: __________________
Exercises 1
Directions: In the figure, 𝑚∠9 = 80° and 𝑚∠5 = 68° . Find the measure of each angle and give a
justification. Must use at all angle relationships at least twice.
𝑚∠1 = _______ because
𝑚∠2 = _______ because
𝑚∠3 = _______ because
𝑚∠4 = _______ because
𝑚∠5 = _______ because
𝑚∠6 = _______ because
𝑚∠7 = _______ because
𝑚∠8 = _______ because
𝑚∠9 = _______ because
𝑚∠10 = _______ because
𝑚∠11 = _______ because
𝑚∠12 = _______ because
𝑚∠13 = _______ because
𝑚∠14 = _______ because
𝑚∠15 = _______ because
𝑚∠16 = _______ because
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Directions: Find each variable and give reasons to only the setup of the equations.
Setup
Rationale
X – Value
Y – Value
Directions: Find each variable and give reasons to only the setup of the equations.
Setup
Rationale
X – Value
Y – Value
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Unit 1B – Angles and Parallel Lines
Name: __________________
Exercises 2
Directions: In the figure, ∠3 = 102° . Find the measure of each angle and give a justification.
Must use at all angle relationships at least twice.
𝑚∠1 = _______ because
𝑚∠2 = _______ because
𝑚∠3 = _______ because
𝑚∠4 = _______ because
𝑚∠5 = _______ because
𝑚∠6 = _______ because
𝑚∠7 = _______ because
𝑚∠8 = _______ because
𝑚∠9 = _______ because
𝑚∠10 = _______ because
𝑚∠11 = _______ because
𝑚∠12 = _______ because
𝑚∠13 = _______ because
𝑚∠14 = _______ because
𝑚∠15 = _______ because
𝑚∠16 = _______ because
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Directions: Find each variable and give reasons to only the setup of the equations.
Setup
Rationale
X – Value
Y – Value
Directions: Find each variable and give reasons to only the setup of the equations.
Setup
Rationale
X – Value
Y – Value
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Unit 1B – Angles and Parallel Lines
Name: __________________
Exercises 3
Directions: Find each variable and give reasons to only the setup of the equations.
Setup
Rationale
X – Value
Y – Value
Directions: Find each variable and give reasons to only the setup of the equations.
Setup
Rationale
X – Value
Y – Value
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Directions: Find each variable and give reasons to only the setup of the equations.
Setup
Rationale
X – Value
Y – Value
Directions: Find each variable and give reasons to only the setup of the equations.
Setup
Rationale
X – Value
Y – Value
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