Question

in two non parallel sides of trapezium are equal then it is cyclic​?

Answer 1

Answer:

no because its opposite angle sum is not 180

Answer 2

Answer:

Hey mate here is your answer___

If the non-parallel sides of a trapezium are equal, prove that it is cyclic.

Asked on October 15, 2019 byavatar

Anubha Pawar

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