Concept explainers
Whether the figure with given vertices is a trapezoid.
Answer to Problem 12PPS
ABCD is a trapezoid.
The lengths are not equal, hence ABCD is not an isosceles trapezoid.
Explanation of Solution
Given:
The given vertices are:
Calculation:
Draw the quadrilateral using given vertices:
A trapezoid has exactly one pair of opposite sides.
Use the slope formula to compare the opposite sides:
The slope of AB will be:
The slope of BC will be:
The slope of CD will be:
The slope of AD will be:
The slopes of exactly one pair of opposite sides are equal, so exactly one pair of opposite sides is parallel.
Hence, ABCD is a trapezoid.
Now, apply the Distance Formula to compare the lengths:
The length of AB will be:
The length of CD will be:
The lengths are not equal, hence ABCD is not an isosceles trapezoid.
Chapter 6 Solutions
Geometry, Student Edition
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