If a point divides a line segment into two congruent line segments, then the point is a midpoint. Point P divides I.H into two congruent line segments.
If a point divides a line segment into two congruent line segments, then the point is a midpoint. Point P divides I.H into two congruent line segments.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Question
18
![In Exercises 1–6, describe the pattern. Then write or draw the next two numbers, letters, or figures. (See Example 1.)
1.
\[ 1, \, -2, \, 3, \, -4, \, 5, \, \ldots \]
2.
\[ 0, \, 2, \, 6, \, 12, \, 20, \, \ldots \]
3.
\[ Z, \, Y, \, X, \, W, \, \ldots \]
4.
\[ A, \, D, \, G, \, J, \, M, \, \ldots \]
5.
\[ \text{Image of polygons progressing in number of sides from triangle to hexagon} \]
6.
\[ \text{Image of stacked cubes increasing by one row and one cube in each set} \]
In Exercises 7–10, make and test a conjecture about the given quantity. (See Example 2.)
7.
The sum of an even integer and an odd integer
8.
The product of any two even integers
9.
The quotient of a number and its reciprocal
10.
The quotient of two negative integers
In Exercises 11–14, find a counterexample to show that the conjecture is false. (See Example 3.)
11.
The product of two positive numbers is always greater than either number.
12.
If \( n \) is a nonzero integer, then \( \frac{n+1}{n} \) is always greater than 1.
13.
If two angles are supplements of each other, then one of the angles must be acute.
14.
A line \( l \) divides \( \triangle MNT \) into two line segments. So, the line is a segment bisector of \( \triangle MNT \).
In Exercises 15–18, use the Law of Detachment to find whether you can conclude the given conclusion from the given statements, if possible. (See Example 4.)
15.
If you download a GIF, then your device crashes. Conclusion: You download a GIF.
16.
If a file is an mp3, then you can delete it. Conclusion: You can delete a file.
17.
If a quadrilateral is a square,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F190d6977-2ae2-4a51-aa5b-fbc1e2d73150%2Fecaab52f-4ad0-43cd-ac35-6ed3e939f1c7%2F78c1a5i_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In Exercises 1–6, describe the pattern. Then write or draw the next two numbers, letters, or figures. (See Example 1.)
1.
\[ 1, \, -2, \, 3, \, -4, \, 5, \, \ldots \]
2.
\[ 0, \, 2, \, 6, \, 12, \, 20, \, \ldots \]
3.
\[ Z, \, Y, \, X, \, W, \, \ldots \]
4.
\[ A, \, D, \, G, \, J, \, M, \, \ldots \]
5.
\[ \text{Image of polygons progressing in number of sides from triangle to hexagon} \]
6.
\[ \text{Image of stacked cubes increasing by one row and one cube in each set} \]
In Exercises 7–10, make and test a conjecture about the given quantity. (See Example 2.)
7.
The sum of an even integer and an odd integer
8.
The product of any two even integers
9.
The quotient of a number and its reciprocal
10.
The quotient of two negative integers
In Exercises 11–14, find a counterexample to show that the conjecture is false. (See Example 3.)
11.
The product of two positive numbers is always greater than either number.
12.
If \( n \) is a nonzero integer, then \( \frac{n+1}{n} \) is always greater than 1.
13.
If two angles are supplements of each other, then one of the angles must be acute.
14.
A line \( l \) divides \( \triangle MNT \) into two line segments. So, the line is a segment bisector of \( \triangle MNT \).
In Exercises 15–18, use the Law of Detachment to find whether you can conclude the given conclusion from the given statements, if possible. (See Example 4.)
15.
If you download a GIF, then your device crashes. Conclusion: You download a GIF.
16.
If a file is an mp3, then you can delete it. Conclusion: You can delete a file.
17.
If a quadrilateral is a square,
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