To calculate: To show that QRST is a trapezoid and determine whether QRST is an isosceles trapezoid
Answer to Problem 2CYP
Quadrilateral QRST is a trapezium, but not an isosceles trapezoid
Explanation of Solution
Given: Quadrilateral QRST has vertices
Formula Used:
Slope of line joining two points
When slope of two lines are equal, then the lines are parallel to each other
When product of slope of two lines is equal to
Quadrilateral is a trapezium if exactly one pair of opposite sides are parallel
Calculation:
Given a quadrilateral QRST has vertices
Slope of sides of quadrilateral are calculated as follows:
Since slope of sides
Thus, sides
In quadrilateral QRST, since exactly one pair of opposite sides are parallel, thus the quadrilateral is a trapezium
Now, using distance formula, let’s compare the length of non-parallel sides
Since the length of sides are not equal, thus trapezium is not an isosceles trapezoid
Conclusion:
Hence, quadrilateral QRST is a trapezium, but not an isosceles trapezoid
Chapter 6 Solutions
Geometry, Student Edition
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