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Transcript
Lesson 7
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
GEOMETRY
Lesson 7: Solve for Unknown Anglesโ€”Transversals
Classwork
Opening Exercise
Use the diagram at the right to determine ๐‘ฅ and ๐‘ฆ.
โƒ–๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝโƒ—
๐ถ๐ท are straight lines.
๐ด๐ต and โƒ–๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝโƒ—
๐‘ฅ=
๐‘ฆ=
Name a pair of vertical angles:
Find the measure of โˆ ๐ต๐‘‚๐น. Justify your calculation.
Discussion
Given line ๐ด๐ต and line ๐ถ๐ท in a plane (see the diagram below), a third line ๐ธ๐น is called a transversal if it intersects โƒ–๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝโƒ—
๐ด๐ต at a
single point and intersects โƒ–๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝโƒ—
๐ถ๐ท at a single but different point. Line ๐ด๐ต and line ๐ถ๐ท are parallel if and only if the following
types of angle pairs are congruent or supplementary.
๏‚ง
Corresponding angles are equal in measure
๏‚ง
Alternate interior angles are equal in measure
๏‚ง
Same side interior angles are supplementary
Lesson 7:
Date:
Solve for Unknown Anglesโ€”Transversals
10/15/14
© 2014 Common Core, Inc. Some rights reserved. commoncore.org
S.39
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 7
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
GEOMETRY
Examples
1.
2.
mโˆ ๐‘Ž =
mโˆ ๐‘ =
3.
4.
mโˆ ๐‘ =
5.
mโˆ ๐‘‘ =
An _________________________________is sometimes useful when solving for unknown angles.
In this figure, we can use the auxiliary line to find the measures of โˆ ๐‘’ and โˆ ๐‘“ (how?), then add the two measures
together to find the measure of โˆ ๐‘Š.
What is the measure of โˆ ๐‘Š?
Lesson 7:
Date:
Solve for Unknown Anglesโ€”Transversals
10/15/14
© 2014 Common Core, Inc. Some rights reserved. commoncore.org
S.40
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 7
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
GEOMETRY
Exercises
In each exercise below, find the unknown (labeled) angles. Give reasons for your solutions.
1.
mโˆ ๐‘Ž =
mโˆ ๐‘ =
mโˆ ๐‘ =
2.
mโˆ ๐‘‘ =
3.
mโˆ ๐‘’ =
mโˆ ๐‘“ =
4.
mโˆ ๐‘” =
5.
mโˆ โ„Ž =
6.
mโˆ ๐‘– =
Lesson 7:
Date:
Solve for Unknown Anglesโ€”Transversals
10/15/14
© 2014 Common Core, Inc. Some rights reserved. commoncore.org
S.41
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 7
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
GEOMETRY
7.
mโˆ ๐‘— =
mโˆ ๐‘˜ =
mโˆ ๐‘š=
8.
mโˆ ๐‘› =
9.
mโˆ ๐‘ =
mโˆ ๐‘ž =
10.
mโˆ ๐‘Ÿ =
Relevant Vocabulary
Alternate Interior Angles: Let line ๐‘ก be a transversal to lines ๐‘™ and ๐‘š such that ๐‘ก intersects ๐‘™ at point ๐‘ƒ and intersects ๐‘š
at point ๐‘„. Let ๐‘… be a point on line ๐‘™ and ๐‘† be a point on line ๐‘š such that the points ๐‘… and ๐‘† lie in opposite half-planes
of ๐‘ก. Then โˆ ๐‘…๐‘ƒ๐‘„ and โˆ ๐‘ƒ๐‘„๐‘† are called alternate interior angles of the transversal ๐‘ก with respect to line ๐‘š and line ๐‘™.
Corresponding Angles: Let line ๐‘ก be a transversal to lines ๐‘™ and ๐‘š. If โˆ ๐‘ฅ and โˆ ๐‘ฆ are alternate interior angles, and โˆ ๐‘ฆ
and โˆ ๐‘ง are vertical angles, then โˆ ๐‘ฅ and โˆ ๐‘ง are corresponding angles.
Lesson 7:
Date:
Solve for Unknown Anglesโ€”Transversals
10/15/14
© 2014 Common Core, Inc. Some rights reserved. commoncore.org
S.42
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 7
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
GEOMETRY
Problem Set
Find the unknown (labeled) angles. Give reasons for your solutions.
1.
mโˆ ๐‘Ž =
2.
mโˆ ๐‘ =
mโˆ ๐‘ =
3.
mโˆ ๐‘‘ =
mโˆ ๐‘’ =
4.
mโˆ ๐‘“ =
Lesson 7:
Date:
Solve for Unknown Anglesโ€”Transversals
10/15/14
© 2014 Common Core, Inc. Some rights reserved. commoncore.org
S.43
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.