Question

ABCD is a quadrilateral in AB = CD and AD=BC .Show that it is a parallelogram.
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Answer 1

Step-by-step explanation:

We Know that,

The opposite sides of parallelogram are equal.

Therefore, quadrilateral ABCD is a parallelogram.

Answer 2

Step-by-step explanation:

In a parallelogram opposite sides are equal and parallel.

Here AB=CD and AD=BC are given so,we can say that the opposite sides are equal.

Draw 2 diagonals AC and DB

we get two triangles, ️ ABC,️ ADC,️ ABD and ️ DCB

In ️ ABC and ️ ADC

AD=BC

AB=DC

AC=AC

Therefore, by sss property,

️ ADC=️ ACB

• Therefore, < DAC=< DCA
• ie,AB parallel to DC
• In ️ ABD and ️ DCB,
• AD=BC
• AB=DC
• DB=DB
• Therefore, ️ ABD=️ DCB
• ie,AD parallel to BC
• THE OPPOSITE SIDES ARE EQUAL AND PARALLEL IN THIS QUADRILATERAL, SO WE HAVE TO SAID THAT ABCD IS A PARALLELOGRAM