
Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
expand_more
expand_more
format_list_bulleted
Concept explainers
Topic Video
Question
QUestion15

The diagram features two quadrilaterals on a coordinate plane:
1. Quadrilateral \(ABCD\) positioned in the first quadrant.
2. Quadrilateral \(JKLM\) positioned in the third quadrant.
### Axes:
- **X-axis**: Horizontal axis of the coordinate plane
- **Y-axis**: Vertical axis of the coordinate plane
### Vertices:
- **\(ABCD\)**:
- \(A\) is positioned at top right.
- \(B\) is located slightly below and to the left of \(A\).
- \(C\) is below \(B\).
- \(D\) is to the right of \(C\).
- **\(JKLM\)**:
- \(J\) is positioned to the top right.
- \(K\) is to the left of \(J\).
- \(L\) is below \(K\).
- \(M\) is right of \(L\).
### Given Angles:
- \(\angle A = 82^\circ\)
- \(\angle B = 104^\circ\)
- \(\angle L = 121^\circ\)
### Unknown Angle:
- \(\angle M\)
The task is to determine the measure of \(\angle M\).
Given the angles and the nature of rigid motions, which preserve angles and relative side lengths:
- Rigid motions include translations, rotations, and reflections.
- The sum of angles in any quadrilateral is \(360^\circ\).
### Calculation:
Sum of angles in \(JKLM\):
\[ \angle J + \angle K + \angle L + \angle M = 360^\circ \]
Given:
\[ \angle J \equiv \angle A = 82^\circ \]
\[ \angle K \equiv \angle B = 104^\circ \]
\[ \angle L = 121^\circ \]
To find \(\angle M\):
\[ 82^\circ + 104^\circ + 121^\circ + \angle M = 360^\circ \]
\[ 307^\circ + \angle M = 360^\circ \]
\[ \angle M = 360](https://content.bartleby.com/qna-images/question/feb8ca9d-9969-400c-8a44-95370ebd76d8/635757d9-d650-43ab-a651-64e0947897c7/af9ems_thumbnail.png)
Transcribed Image Text:**Understanding Rigid Motions in Geometry**
In the diagram below, a sequence of rigid motions maps the quadrilateral \(ABCD\) onto \(JKLM\).

The diagram features two quadrilaterals on a coordinate plane:
1. Quadrilateral \(ABCD\) positioned in the first quadrant.
2. Quadrilateral \(JKLM\) positioned in the third quadrant.
### Axes:
- **X-axis**: Horizontal axis of the coordinate plane
- **Y-axis**: Vertical axis of the coordinate plane
### Vertices:
- **\(ABCD\)**:
- \(A\) is positioned at top right.
- \(B\) is located slightly below and to the left of \(A\).
- \(C\) is below \(B\).
- \(D\) is to the right of \(C\).
- **\(JKLM\)**:
- \(J\) is positioned to the top right.
- \(K\) is to the left of \(J\).
- \(L\) is below \(K\).
- \(M\) is right of \(L\).
### Given Angles:
- \(\angle A = 82^\circ\)
- \(\angle B = 104^\circ\)
- \(\angle L = 121^\circ\)
### Unknown Angle:
- \(\angle M\)
The task is to determine the measure of \(\angle M\).
Given the angles and the nature of rigid motions, which preserve angles and relative side lengths:
- Rigid motions include translations, rotations, and reflections.
- The sum of angles in any quadrilateral is \(360^\circ\).
### Calculation:
Sum of angles in \(JKLM\):
\[ \angle J + \angle K + \angle L + \angle M = 360^\circ \]
Given:
\[ \angle J \equiv \angle A = 82^\circ \]
\[ \angle K \equiv \angle B = 104^\circ \]
\[ \angle L = 121^\circ \]
To find \(\angle M\):
\[ 82^\circ + 104^\circ + 121^\circ + \angle M = 360^\circ \]
\[ 307^\circ + \angle M = 360^\circ \]
\[ \angle M = 360
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution
Trending nowThis is a popular solution!
Step by stepSolved in 3 steps with 3 images

Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.Similar questions
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage Learning

Elementary Geometry For College Students, 7e
Geometry
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Cengage,

Elementary Geometry for College Students
Geometry
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Cengage Learning