The information needed to prove that a quadrilateral is a parallelogram.
Answer to Problem 45HP
To prove that a quadrilateral is a parallelogram, it has to be shown that the opposite sides are parallel.
Explanation of Solution
Consider a quadrilateral named as ABCD in which lines AB and CD are parallel.
The opposite sides of a parallelogram are parallel.
From the above sentence, only one pair of opposite sides is parallel.
A quadrilateral ABCD is a parallelogram, if the other pair of opposite sides is also parallel.
The second condition will be that the other pair i.e. AD and BC are also parallel and congruent to each other.
So,
To prove that a quadrilateral is a parallelogram, it has to be shown that the opposite sides are parallel.
Chapter 6 Solutions
Geometry, Student Edition
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