Question

if non paralles sides of a trapzium are equal prove thar it is cycle​

Answer 1

Answer:

I have mentioned the answer in the pic..

hope it helps..

Answer 2

Given

ABCD is 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 triangle DAM and triangleCBN,

AD=BC [Given]

∠AMD=∠BNC [Right angles]

DM=CN [Distance between the parallel lines]

Therefore, triangle DAM ≅ triangle CBN by RHS congruence condition

Now, ∠A=∠B [by CPCT]

Also, ∠B+∠C=180° ....[Sum of the co-interior angles]

similarly

=>∠A+∠C=180

thus proved ABCD is a cyclic quadrilateral