Concept explainers
Whether JKLM is a rhombus, a rectangle or a square.
Answer to Problem 20PPS
QRST is a rhombus.
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:
Both of these diagonals are not congruent, hence, QRST is not a rectangle.
Finding the slope of JL:
Finding the slope of KM:
As,
Hence, QRST is a rhombus.
Chapter 6 Solutions
Geometry, Student Edition
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