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 opposite side of a parallelogram are equal.Prove

Asked by Varsha 13th June 2016, 8:29 PM
Answered by Expert
Answer:
By space Parallelogram space definition comma space line space AB space is space parallel space to space line space CD space and space line space BC space is space parallel space to space line space DA. space space space
We space are space required space to space prove space that space AB space equals space CD space and space BC space equals space DA. space
Let space AC space be space the space diagonal space of space parallelogram. space
Consider space two space triangles space ABC space and space CDA space as space shown space in space figure. space space
space In space increment ABC space and space increment CDA comma space space
1. space angle CAB equals angle ACD space..... left parenthesis The space line space AC space is space straight a space transversal space of space parallel space lines space AB space and space CD comma space hence angle CAB space and space angle ACD space are space alternate space angles right parenthesis space space space
2. space angle ACB equals angle CAD space..... left parenthesis The space line space AC space is space straight a space transversal space of space parallel space lines space BC space and space DA comma space hence space angle space ACB space and angle CAD space are space alternate space angles right parenthesis space space
3. space AC equals CA space..... left parenthesis The space common space side space to space the space two space triangles right parenthesis space space space
From space conditions space 1 comma 2 space and space 3 comma space space space
increment ABC space approximately equal to space increment CDA space left parenthesis By space Angle space minus Side minus Angle space congruency space property right parenthesis space space
Hence space as space triangles space are space congruent space triangles space comma
So comma space the space corresponding space sides space are space equal comma space space
rightwards double arrow AB space equals space CD space and space BC space equals space DA. space
Answered by Expert 14th June 2016, 9:09 AM
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