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Geometry Packet 2: Parallel & Perpendicular Lines Date Topic 5-Sep Lines and Angles Parallel Lines and Related Angles
Standards
I will… Assignments identify relationships between Lesson Check #1-10 figures in space and identify angles formed by two lines and a transversal.
MAFL.912.G-CO.1.1 MAFL.912.G-CO.3.9 MAFL.912.G-CO.4.12
6-Sep Properties of Parallel Lines
MAFL.912.G-CO.3.9
7-Sep Mixed Review 8-Sep Quiz
MAFL.912.G-CO.1.1 MAFL.912.G-CO.3.9 MAFL.912.G-CO.4.12
prove theorem about parallel lines and use properties of parallel lines to find angle measures.
Lesson Check #1-6
Assignments listed for this week are due at the beginning of the period today.
11-Sep Parallel and Perpendicular Lines
MAFL.912.G-MG.1.3
relate parallel and perpendicular Lesson Check #1-5 lines.
12-Sep Parallel Lines and Triangles
MAFL.912.G-CO.3.10
use parallel lines to prove a Lesson Check #1-8 theorem about triangles and find measures of angles of triangles.
13-Sep Constructing Parallel and Perpendicular Lines
MAFL.912.G-CO.4.12 MAFL.912.G-CO.4.13
construct parallel and perpendicular lines.
14-Sep Mixed Review 15-Sep Quiz
MAFL.912.G-CO.3.10 MAFL.912.G-CO.4.12 MAFL.912.G-CO.4.13 MAFL.912.G-MG.1.3
18-Sep Slopes of Parallel and Perpendicular Lines
MAFL.912.G-GPE.2.5
19-Sep Review for Test
ALL OF THE ABOVE
Practice & Problem-Solving Exercises #7-17, 22-33, 41-46 <28>
20-Sep Test
ALL OF THE ABOVE
PACKET DUE TODAY! This includes completed answers to the Essential Questions & Vocabulary.
Lesson Check #1-6
Assignments listed for this week are due at the beginning of the period today. relate slope to parallel and perpendicular lines.
1
Lesson Check #1-6
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Geometry Packet 2: Parallel & Perpendicular Lines Essential Questions • How do you prove that two lines are parallel?
•
What is the sum of the measures of the angles of a triangle?
•
How do you write an equation of a line in the coordinate plane?
Vocabulary TERM
DEFINITION
EXAMPLE OR VISUAL
Alternate exterior angles
Alternate interior angles
Corresponding angles
Exterior angle of a polygon
Parallel lines
Perpendicular lines
Same-side interior angles
Skew lines
Transversal
2
Name
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Geometry Packet 2: Parallel & Perpendicular Lines TOPIC 1: Lines & Angles Essential Understanding • Not all lines and not all planes intersect. Key Concept: Parallel & Skew Parallel lines are coplanar lines that do not intersect. The symbol || means “is parallel to.”. Skew lines are noncoplanar; they are not parallel and do not intersect.
Parallel planes are planes that do not intersect. Example 1
3
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Geometry Packet 2: Parallel & Perpendicular Lines Got it? A
Essential Understanding • When a line intersects two or more lines, the angles formed at the intersection points create special angle pairs. Transversals • A transversal is a line that intersects two or more coplanar lines at distinct points. Key Concept: Angle Pairs Formed by Transversals Alternate interior angles are
nonadjacent interior angles that lie on opposite sides of the transversal. Same-side interior angles are
interior angles that lie on the same side of the transversal.
Corresponding Correspondingangles angleslie lieon onthe same sideside of the the same of transversal the transversal and in positions. and in corresponding corresponding positions.
Alternate exterior angles are
nonadjacent exterior angles that lie on opposite sides of the transversal.
4
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Date
Geometry Packet 2: Parallel & Perpendicular Lines Example 2
Got it? B
Example 3
Got it? C
5
Period
Name
Date
Geometry Packet 2: Parallel & Perpendicular Lines Lesson Check
(show work below)
6
Period
Name
Date
Geometry Packet 2: Parallel & Perpendicular Lines TOPIC 2 Concept Byte: Parallel Lines & Related Angles
7
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Geometry Packet 2: Parallel & Perpendicular Lines TOPIC 2: Properties of Parallel Lines Essential Understanding • The special angle pairs formed by parallel lines and a transversal are congruent, supplementary, or both. Same-Side Interior Angles Postulate (SSIAP) If a transversal intersects two
parallel lines, then sameside interior angles are
supplementary.
Example 1
Got it? A
Alternate Interior Angles Theorem (AIAT) If a transversal intersects two
parallel lines, then alternate interior angles are
congruent.
8
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Geometry Packet 2: Parallel & Perpendicular Lines Corresponding Angles Theorem (CAT) If a transversal intersects two
parallel lines, then corresponding angles are
congruent.
Example 2
Got it? B
9
Period
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Date
Geometry Packet 2: Parallel & Perpendicular Lines Alternate Exterior Angles Theorem (AEAT) If a transversal intersects two
parallel lines, then alternate exterior angles are congruent.
Example 3
Got it? C
10
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Geometry Packet 2: Parallel & Perpendicular Lines Example 4
Got it? D
11
Period
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Date
Geometry Packet 2: Parallel & Perpendicular Lines Lesson Check
(show work below)
12
Period
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Date
Period
Geometry Packet 2: Parallel & Perpendicular Lines TOPIC 3: Parallel & Perpendicular Lines Essential Understanding • You can use the relationships of two lines to a third line to decide whether the two lines are parallel or perpendicular to each other. Theorems If two lines are parallel to the
same line, then they are parallel to each other.
In a plane, if two lines are
perpendicular to the same line, then they are parallel to each other.
Example 1
Got it? A
13
Name
Date
Geometry Packet 2: Parallel & Perpendicular Lines Perpendicular Transversal Theorem In a plane, if a line is
perpendicular to one of two parallel lines, then it is also perpendicular to the other.
Example 2
Got it? B
14
Period
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Date
Geometry Packet 2: Parallel & Perpendicular Lines Lesson Check
(show work below)
15
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Geometry Packet 2: Parallel & Perpendicular Lines TOPIC 4: Parallel Lines & Triangles Essential Understanding • The sum of the angle measures of a triangle is always the same. Parallel Postulate Through a point not on a line, there is one and only one line parallel to the given line.
There is exactly one line through 𝑃 parallel to ℓ. Triangle Angle-Sum Theorem The sum of the measures of the angles of a triangle is 𝟏𝟖𝟎 °.
𝟏𝟖𝟎 ° Example 1
Got it? A
16
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Geometry Packet 2: Parallel & Perpendicular Lines Key Concept: Polygon Angles An exterior angle of a polygon is an angle formed by a side and an extension of an adjacent side. For each exterior angle of a triangle, the two nonadjacent interior angles are its remote interior angles. In each triangle below, ∠1 is an exterior angle and ∠2 and ∠3 are its remote
interior angles.
Triangle Exterior Angle Theorem The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.
Example 2
Got it? B
17
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Date
Geometry Packet 2: Parallel & Perpendicular Lines Example 3
Got it? C
18
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Date
Geometry Packet 2: Parallel & Perpendicular Lines Lesson Check
(show work below)
19
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Date
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Geometry Packet 2: Parallel & Perpendicular Lines TOPIC 5: Constructing Parallel & Perpendicular Lines Essential Understanding • You can use a straightedge and a compass to construct parallel and perpendicular lines. Example 1
Got it? A
Example 2
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Date
Geometry Packet 2: Parallel & Perpendicular Lines Got it? B
Example 3
Got it? C
21
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Geometry Packet 2: Parallel & Perpendicular Lines Perpendicular Postulate Through a point not on a line, there is one and only one line perpendicular to the given line.
There is exactly one line through 𝑃 perpendicular to ℓ. Example 4
Got it? D
22
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Geometry Packet 2: Parallel & Perpendicular Lines Lesson Check
(show work below)
23
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Date
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Geometry Packet 2: Parallel & Perpendicular Lines TOPIC 6: Slopes of Parallel & Perpendicular Lines Essential Understanding • You can determine whether two lines are parallel or perpendicular by comparing their slopes. Key Concept: Slopes of Parallel Lines • If two nonvertical lines are parallel, then their slopes are equal. • If the slopes of two distinct nonvertical lines are equal, then the lines are parallel. • Any two vertical lines or horizontal lines are parallel. Example 1
Got it? A
Example 2
Got it? B
24
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Geometry Packet 2: Parallel & Perpendicular Lines Key Concept: Slopes of Perpendicular Lines • If two nonvertical lines are perpendicular, then the product of their slopes is -1. • If the slopes of two lines have a product of -1, then the lines are perpendicular. • Any horizontal line and vertical line are perpendicular. Example 3
Got it? C
Example 4
Got it? D
25
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Geometry Packet 2: Parallel & Perpendicular Lines Example 5
Got it? E
26
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Geometry Packet 2: Parallel & Perpendicular Lines Lesson Check
(show work below)
27
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Geometry Packet 2: Parallel & Perpendicular Lines Practice & Problem-Solving Exercises
28
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Geometry Packet 2: Parallel & Perpendicular Lines
29
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Geometry Packet 2: Parallel & Perpendicular Lines
(show work below)
30
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