Question

In figure, ABCD is a quadrilateral in which BC=AD and angle ADC = angle BCD. Show that AC=BD and angle ACD = angle BDC​

Answer 1

Answer:

ABCD is a quadrilateral in which AD=BC and ∠ADC = ∠BCD.

To prove : ABCD lies on a circle i.e they are concyclic.

Join AC and BD .

Now in ∆ADC and ∆BDC,

AD = BC (given)

∠ADC =∠BDC (given)

DC= DC (common)

∆ADC≅∆BDC ( SAS congruency)

∠DAC =∠DBC ( by CPCT )

Hence the angle made by a segment on the other part of the circle are equal.

Hence A,B,C,D must lie on a circle.