Question

На стороне ВС параллелограмма АВСД взята точка М так,что АВ>ВМ. а) докажите,что АМ биссектриса угла ВАД,б) найдите периметр параллелограмма, если СД=8 см,СМ=6 см ДАЮ 25 БАЛЛОВ!

Answer 1

1) проведем ОМ параллельно АВ. У параллелограмма противоположные углы равны, т.е. угол О равен углу В. имеем два равносторонних треугольника с общим основанием АМ (+угол напротив основания) и равными боковыми сторонами. Значит угол КАМ равен углу МАВ. Отсюда следует, что АМ биссектриса угла ВАД

2)сторона АВ=СД=8см. АВ=ВМ=8см. СМ=4см, тогда ВС=ВМ+СМ=8+4=12см. Периметр параллелограмма 2*(8+12)=40см.

Answer 2

Proof that AM is the angle bisector of angle VAD

To prove that AM is the angle bisector of angle VAD, we need to show that angle BAM is congruent to angle MAD.

Since AB is parallel to CD in parallelogram ABCD, we can conclude that angle BAM is congruent to angle CDM because they are corresponding angles.

Similarly, angle MAD is congruent to angle CMA because they are corresponding angles.

Therefore, we have angle BAM congruent to angle CDM and angle MAD congruent to angle CMA.

By the transitive property of congruence, we can conclude that angle BAM is congruent to angle MAD.

Hence, AM is the angle bisector of angle VAD.

Finding the perimeter of the parallelogram

To find the perimeter of the parallelogram, we need to know the lengths of its sides. Unfortunately, the lengths of sides AB and AD are not provided in the question. Therefore, we cannot calculate the perimeter of the parallelogram based on the given information.

If you can provide the lengths of sides AB and AD, I would be happy to help you calculate the perimeter of the parallelogram.

Please note that the lengths of sides CD and CM are given as 8 cm and 6 cm respectively, but these lengths alone are not sufficient to determine the perimeter of the parallelogram.