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using statements and proofs how to prove that in parallelogram abcd that is cut by a diagnoal line bd that the perimeter of abc is equal to the perimeter of adc

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2 Answers

Gray,
 
Here is another approach.  After drawing the parallelogram try to prove that the two triangles formed by drawing the diagonal are congruent.  Since we have a parallelogram we already know that AB=CD and that BC=DA. Since the diagonal BD is the same line for both triangles then we can prove congruency by SIDE SIDE SIDE.  Congruent triangles have equal perimeters.
Draw a parallelogram abcd first.
 
Since for any parallelogram, the opposite sides are congruent. Therefore, you have
ad = cb
ab = cd
 
But db = bd (reflexive property)
 
Adding the above three equations gives
ad+ab+db = cb+cd+bd
 
Therefore, you proved that the perimeter of abc is equal to the perimeter of adc.