prove that cyclic trapezium is isosceles
Answers
Step-by-step explanation:
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Given : cyclic trapezium is an isosceles trapezium
To Fine : prove
Solution:
Let say ABCD is a cyclic trapezium where
AD || BC
Hence we need to show that AB = CD for it to be an isosceles trapezium
as its cyclic => sum of opposite angles = 180°
Lets extend AD and draw a line parallel to AB passing through C and intersecting extended AD at E.
AB || CD and CE || AB
hence ABCE is a parallelogram
=> AB = CE opposite sides are equal
in parallelogram opposite angles are equal
Hence ∠B = ∠E
∠B + ∠D = 180° ( cyclic Quadrilateral )
∠D + ∠CDE = 180° linear Pair
=> ∠E = ∠CDE
in ΔCDE
∠E = ∠CDE
=> CD = CE
AB = CE ( opposite sides of parallelogram )
=> AB = CD
Hence trapezium is isosceles trapezium
QED
Hence proved
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