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if a non-parallel sides of a trapezium are equal. Then prove that it is cyclic.
Answers
Answer:if non parallel sides are equal then the trapezium will become a rectangle and it will be a cyclic quad
Step-by-step explanation:
Maths
If the non-parallel sides of a trapezium are equal, prove that it is cyclic.
October 15, 2019avatar
Anubha Pawar
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VIDEO EXPLANATION
ANSWER
Given:
ABCDABCD is a trapezium where non-parallel sides AD and BC are equal.
Construction:
DMDM and CNCN are perpendicular drawn on ABAB from DD and CC respectively.
To prove:
ABCDABCD is cyclic trapezium.
Proof:
In \triangle DAM△DAM and \triangle CBN△CBN,
AD = BCAD=BC ...Given
∠AMD = ∠BNC∠AMD=∠BNC ...Right angles
DM = CNDM=CN ...Distance between the parallel lines
\triangle DAM ≅ \triangle CBN△DAM≅△CBN by RHS congruence condition.
Now,
∠A = ∠B∠A=∠B ...by CPCT
Also, ∠B + ∠C = 180°∠B+∠C=180° ....Sum of the co-interior angles
⇒ ∠A + ∠C = 180°⇒∠A+∠C=180°
Thus, ABCDABCD is a cyclic quadrilateral as sum of the pair of opposite angles is 180°180°.
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