Question

give me answer if you know plz

Answer 1

bit short answer i hope it will help u

Answer 2

Heya dear  !!
______________________________________________________________

Question : ABCD is a trapezium  with AB||DC , the diagonals AC  and BD  are interecting  at E . If  ΔAED is similar to ΔBEC , then prove that AD = BC 
______________________________________________________________

Solution : 

Given : ABCD is a trapezium , AB║CD . Diagonals AC and BD intersect at E 

To Prove : ΔAED ≈ ΔBEC 

Given : ΔAED ≈ ABEC

⇒ AE/ BE = ED/EC = AD/BC ________(1)  { corresponding sides are proportional } 

In ΔABE and ΔCDE 

∠ABE = ∠CED { vertically opposite angles }

∠EAB = ∠ECD { Alternate angle } 

∴ΔABE ≈ ΔCDE { AA similarity }

⇒ AB/CD = EB/ED = AE/EC  { corresponding sides are proportional } 

⇒ EC/ED = AE/EB _____(2)

From (1) and (2) 

⇒ EC/ED = ED/EC 

⇒ EC² = ED² 

⇒ EC = ED 

From (1) we get , 

AD/BC = ED/EC 

⇒ AD/BC = 1 

⇒ AD = BC  { ∵ ED = EC } 

Hence proved 
____________________________________________________________