Question

In the figure ABCD is an isosceles trapezium prove that ABCD is cyclic

Answer 1

Answer:

bhai figure kaha hai without figure ka solution kese hoga.

Hum khud se figure bna kr solution de rhe hai ok

Step-by-step explanation:

Given A trapezium ABCD in which AB // DC and AD = BC

To prove angle A + angle C = 180° , and angle B + angle D = 180° .

Construction Draw DL |_ AB and CM |_ AB.

Proof from the right ∆s ALD and BMC, we have

AD = BC ( given)

DL = CM ( distance between two parallels)

.•. ∆ ALD ~ ∆ BMC [ RHS - criterion ]

=> angle A = angle B... ( 1 ) and angle ADL = angle BCM ... ( 2 )

=> angle C = angle BCD = angle BCM + 90°

= angle ADL+90° = angle ADC = angle D [ using ( 2 ) ]

=> angle C = angle D ...( 3 )

Now, angle A + angle B + angle C + angle D = 360° [ sum of the angles of a quad. is 360° ]

=> 2( angle A + angle C) = 360° and 2( angle B + angle D) =360° [ using ( 1 ) and ( 3 ) ]

=> angle A + angle C = 180° and angle B + angle D = 180° .

Hence, quad. ABCD is cyclic.

( Proved)

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