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Question
How many unique trapeziums can be drawn given three sides and one angle?
How many unique trapeziums can be drawn given three sides and one angle?
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Solution
The correct option is A 1
To construct a trapezium, draw one of its parallel sides as a base. On that base, construct a triangle with the two more measurements. Now, through the vertex of that triangle, construct the parallel line opposite to the base so that the triangle lies between the parallel sides. The fourth vertex lies
on this parallel line. Mark it with the remaining measure. Thus, we need four independent measurements to construct a trapezium.
Thus, if given three sides and one angle, one and only one trapezium can be constructed.
To construct a trapezium, draw one of its parallel sides as a base. On that base, construct a triangle with the two more measurements. Now, through the vertex of that triangle, construct the parallel line opposite to the base so that the triangle lies between the parallel sides. The fourth vertex lies
on this parallel line. Mark it with the remaining measure. Thus, we need four independent measurements to construct a trapezium.
Thus, if given three sides and one angle, one and only one trapezium can be constructed.
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