Question

Que: If the non-parallel sides of a trapezium are equal, prove that it is cyclic?​

Answer 1

Answer:

Solution:

Contruction-Consider a trapezium ABCD with AB||CD and BC = AD.

Draw AM ⊥CD and BN ⊥ CD

In ∆AMD and ∆BNC;

AD = BC (Given)

∠AMD = ∠BNC (90°)

AM =BN (perpendiculars between parallel lines)

∆AMD = ∆BNC (By RHS congruency)

∆ADC = ∆BCD (By CPCT rule) …….(i)

∠BAD and ∠ADC are on the same side of transversal AD.

∠BAD + ∠ADC = 180° ……(ii)

∠BAD + ∠BCD = 180° (by equation (i))

Since,

the opposite angles are supplementary, therefore, ABCD is a cyclic quadrilateral.

Hope it will be helpful :)☺️

Answer 2

Answer:

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

Explanation:

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