If the non
of trapazium
qual prove that it is cyclic
الملححمم
میمن
مبلمه
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Step-by-step explanation:
Given:
ABCD is a trapezium where non-parallel sides AD and BC are equal.
Construction:
DM and CN are perpendicular drawn on AB from D and C respectively.
To prove:
ABCD is cyclic trapezium.
Proof:
In △DAM and △CBN,
AD=BC ...Given
∠AMD=∠BNC ...Right angles
DM=CN ...Distance between the parallel lines
△DAM≅△CBN by RHS congruence condition.
Now,
∠A=∠B ...by CPCT
Also, ∠B+∠C=180° ....Sum of the co-interior angles
⇒∠A+∠C=180°
Thus, ABCD is a cyclic quadrilateral as sum of the pair of opposite angles is 180°.
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