3) Prove that in a cyclic trapezium angles at the base are congruent.
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Angles at the base are Congruent in a cyclic trapezium
Step-by-step explanation:
Let say ABCD is the cyclic trapezium with AB ║ CD
Now properties of Cyclic Quadrilateral
that sum of opposite angles = 180°
=> ∠BAD + ∠BCD = 180°
now AB ║ CD
& BC intersects it
=> ∠ABC + ∠BCD = 180°
Equating both
=> ∠BAD + ∠BCD = ∠ABC + ∠BCD
=> ∠BAD = ∠ABC
=> ∠A = ∠B
=> Angles at the base are Congruent
QED
Proved
angles at the base are congruent in a cyclic trapezium
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