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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

It is a parallelgram that is cut in half by a diagnoal line making two triangles

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David S. | Wise Math TutorWise Math Tutor
5.0 5.0 (58 lesson ratings) (58)
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.
Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
4.6 4.6 (13 lesson ratings) (13)
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.