Question

hey mates ,☺️

,☝️prove that if the non - parallel sides of a trapezium are equal , then it's a trapezium.

no spams please..I need it ..

Answer 1

In ΔAED and ΔBFC, AD = BC (Given)

DE = CF (Distance between parallel sides is same)

∠AED = ∠BFC = 90° ΔAED ≅ ΔBFC (RHS Congruence criterion)

Hence ∠DAE = ∠CBF (CPCT) … (1)

Since AB||CD, AD is transversal ∠DAE + ∠ADC = 180° (Sum of adjacent interior angles is supplementary)

⇒ ∠CBF + ∠ADC = 180° [from (1)]

Since sum of opposite angles is supplementary in trapezium ABCD.

Thus ABCD is a cyclic trapezium

Answer 2

${\huge {\mathfrak {Answer :-}}}$

✨$<b>To prove that a quadrilateral is cyclic, we simply need to show that the sum of opposite pair of angles is 180°. </b>$ ✨

So, refer to the attachment.. ⬆️⬆️

$<i>$ That's it..
$<marquee >$
${\red {Hope \: it \: helps}}$
$</marquee >$
${\huge {\blue{Thanks..}}}$