Question

is AB=CD and AD=BC in ABCD parallelogram?​

Answer 1

Answer:

yes it's there opposite sides are equal and parallel in parallelogram

Step-by-step explanation:

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Answer 2

${\huge{\bold{\underline{Answer:-}}}}$

It is given that AB=CD and BC=AD. Also, we can see that AC is common in ΔABC and ΔCDAΔABC and ΔCDA. Therefore, as all three sides of ΔABCΔABC are equal to corresponding sides of ΔCDAΔCDA , we can say that both the triangles are congruent by SSS congruence rule.

Therefore, by using CPCT, we can say that:

∠ABC=∠CDA∠CAB=∠ACD..(i)∠DAC=∠BCA..(ii)∠ABC=∠CDA∠CAB=∠ACD...(i)∠DAC=∠BCA..(ii) 

Now if we add equation (i) and equation (ii), we get

∠CAB+∠DAC=∠ACD+∠BCA∠CAB+∠DAC=∠ACD+∠BCA

Now from the figure, we can deduce that ∠CAB+∠DAC=∠DAB∠CAB+∠DAC=∠DAB and ∠ACD+∠BCA=∠BCD∠ACD+∠BCA=∠BCD. Therefore, our equation becomes:

∠DAB=∠BCD∠DAB=∠BCD

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