ABCD is a quadrilateral in which AB = DC and AD = BC AC is a diagonal Prove - Maths - Triangles

Question

ABCD
is a quadrilateral in which AB = DC and AD = BC AC is a diagonal
Prove that AB || CD and AD || BC

Atul Shaw · Accepted Answer

Dear student,In △ABC and △ADC,AB=DC (Given)AD=BC (Given)AC=AC (Common)So, by SSS criterion,  △ABC≅△ADC∠BAC=∠DCA (CPCT)Thus, AB||AC as interior angles are equal
∠DAC=∠ACB (CPCT)Thus, AD||BC as interior angles are equal
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ABCD is a quadrilateral in which AB = DC and AD = BC. AC is a diagonal. Prove that AB || CD and AD || BC.