Question

abcd is a quadilateral with side AB=Cd and AD=BC show that it is a parallelogram? ​

Answer 1

Step-by-step explanation:

As the opposite angles of quadrilateral ABCD are equal, i.e., ∠DAB=∠BCD and ∠ABC=∠CDA , so we can say that quadrilateral ABCD is a parallelogram

Answer 2

$\huge\mathcal\blue{hello}$

Given:In □ABCD

AB=DCandAD=BC

To prove: ABCD is a parallelogram

Construction: Draw diagonal AC and DB.

Proof: in △ABC and △ADC

AD=BC [Given]

AB=DC [Given]

AC=AC [Common side]

∴ By SSS property

△ADC≅△ACB

∴∠DAC=∠DCA

∴AB∣∣DC [By theorem]

In△ABDand△DCB

DB=DB [Common side]

AD=BC [Given]

AB=DC [Given]

∴△ABD≅△DCB

∴AD∣∣BC

Since AB∣∣DC and AD∣∣BC.

△ABCD is parallelogram..

REF IMAGE

$\huge\mathcal\blue{thankyou}$