abcd is a quadilateral in which all the four sides are equal show that ab parelle to cd and ad parellel to bc
Answers
Step-by-step explanation:
proof: Consider a quadrilateral called parallelogram.bcoz, a quadrilateral can be defines as 4 angles and 4 vertices which parallel to each other.
Therefore consider one parallelogram, having four vertices called A, B, C, D. AB drawn parallel to CD. & BC drawn parallel to AD. Then, draw one diagonal from A to C. therefore the parallelogram can be divided into 2 triangles called triangle ABC and triangle ADC.Then extend the base B and draw one perpendicular from C to E ( extended from B).then we got a right angled triangle.apply pythagorus theorem ie, hyp ^2 = base ^ 2 + altitude ^2. ie, AC^2= AE^2+ CE ^2.
Next consider the secomd triangle built by the parallelogram.triangle ADC.In this triangle extend the end D and point it as F.draw perpendicular from A to F.here also we got the right angled triangle, AFC. apply pythagorus theorem theorem AC^2= FC ^2+AF^2. therefore we got AC as the hypotenus for these 2 triangles constructed from the parallellogram.ie, AB parallel to DC and AD parallel to BC.
