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If the non-parallel sides of a trapezium are equal, prove that it is cyclic.
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Given:
is a trapezium where non-parallel sides and are equal.
is a trapezium where non-parallel sides and are equal.
Construction:
and are perpendicular drawn on from and , respectively.
and are perpendicular drawn on from and , respectively.
To prove:
is cyclic trapezium.
is cyclic trapezium.
Proof:
In and ,
...[Given]
...[Right angles]
...[Distance between the parallel lines]
Therefore, by congruence condition.
Now, ...[by CPCT]
Also, ....[Sum of the co-interior angles]
.
Thus, is a cyclic quadrilateral as the sum of the pair of opposite angles is .
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| Question Text | If the non-parallel sides of a trapezium are equal, prove that it is cyclic. |
| Answer Type | Text solution:1 |
| Upvotes | 150 |
