Concept explainers
Whether JKLM is a rhombus, a rectangle or a square.
Answer to Problem 22PPS
QRST is a rectangle, a rhombus and also a square.
Explanation of Solution
Given:
The vertices are:
Calculation:
Plot the vertices on the graph:
According to Rectangle Theorem, if the diagonals of a parallelogram are congruent, then it is a rectangle.
According to Rhombi Theorem, if the diagonals of a parallelogram are perpendicular, then it is a rhombus.
According to Square Theorem, if the quadrilateral is both, a rectangle and a rhombus, then it is a square.
Consider the diagonals of JKLM:
Finding the length of JL:
Finding the length of KM:
The diagonals are congruent, hence, QRST is a rectangle.
Finding the slope of JL:
Finding the slope of KM:
As,
Hence, QRST is a rectangle, a rhombus and also a square.
Chapter 6 Solutions
Geometry, Student Edition
Additional Math Textbook Solutions
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
Probability and Statistics for Engineers and Scientists
Essentials of Statistics (6th Edition)
Elementary Statistics: Picturing the World (7th Edition)
Elementary Statistics
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