Concept explainers
a
The converse, inverse and contrapositive of the each side of the
a
Answer to Problem 2PSA
The following are the answers for the first statement
Converse statement is NOT TRUE Inverse Statement is NOT TRUE Contrapositive statement is NOT TRUE
Explanation of Solution
Given Information: The following statement has been given
If each side of a triangle has a length of 10, then the triangle’s perimeter is 30
We write the following asked statements
- Converse Statement − If a triangle’s perimeter is 30, then each side of the triangle has a length of 10
Hence, the Converse statement is NOT TRUE
- Inverse Statement − If each side of a triangle does not have a length of 10, then the triangle’s perimeter is not 30
- Contrapositive Statement − If a triangle’s perimeter is not 30, then each side of the triangle does not have a length of 10
Hence, the Inverse Statement is NOT TRUE
Hence, the Contrapositive statement is NOT TRUE
b
The converse, inverse and contrapositive of an
b
Answer to Problem 2PSA
The following are the answers for the second statement
Converse statement is TRUE Inverse Statement is TRUE Contrapositive statement is TRUE
Explanation of Solution
Given Information: The following statement has been given
If an angle is acute, then it has a measure greater than zero and less than 90 degrees.
We write the following asked statements
- Converse Statement − If an angle has a measure greater than zero and less than 90 degrees, then it is acute Hence, the Converse statement is TRUE
- Inverse Statement − If an angle is not acute, then it does not have a measure greater than zero and less than 90 degrees.
- Contrapositive Statement − If an angle does not have a measure greater than zero and less than 90 degrees, then it is not acute
Hence, the Inverse Statement is TRUE
Hence, the Contrapositive statement is TRUE
Chapter 1 Solutions
Geometry For Enjoyment And Challenge
Additional Math Textbook Solutions
University Calculus: Early Transcendentals (4th Edition)
Elementary Algebra: Concepts and Applications (10th Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
A Survey of Mathematics with Applications (10th Edition) - Standalone book
Thinking Mathematically (7th Edition)
- 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