Question

Show that the cyclic trapezium is isosceles. Prove with figure.​

Answer 1

Answer:

Explanation:

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Draw a trapezium ABCD with AB<CD. Drop perpendiculars AM and BN on DC. The solution start as follows: 

Given- ABCD is a trapezium with ABIICD and BC=AD(as it is isosceles)

To prove- ABCD is a cyclic quadrilateral 

Construction- Drop perpendiculars AM and BN on DC

Proof-In ΔAMD and ΔBNC

AD=BC(given)

angleAMD=angleBNC=90degree

AM=BN (perpedicular distance between two parallel lines is same)

Therefore, ΔAMD CONGRUENT TO ΔBNC (By RHS congruence rule)

angleADC=angleBCD (CPCT) .... (1)

angleBAD+angleADC=180degree  (angle on the same side of transversal AD) ....

(2)

FROM (1) and (2)

angleBAD+angleBCD=180degree

⇒Opposite angles are supplementary

Therefore, ABCD is a cyclic quadrilateral.

Hence, proved............

Answer 2

Answer:

OPPOSITE ANGLES OF A CYCLIC QUADRILATERAL ARE SUPPLEMENTRY

Hence Proved

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