Question

MP=KP,DM=DK. Докажите, что луч DP - биссектриса угла MDK

Answer 1

Биссектриса это луч, делющий угол пополам. Т.к. стороны равны,получается,что DP это биссектриса угла.

Answer 2

Если DP общая сторона.Значит треугольники равны по 3 сторонам
получается:MDP=KDP
У РАВНЫХ ТРЕУГОЛЬНИКОВ СООТВЕТСТВЕННЫЕ УГЛЫ РАВНЫ, ЗНАЧИТ DP-биссектриса угла MDK

Answer 3

Given Information:

We are given that MP = KP and DM = DK.

To Prove:

We need to prove that the line segment DP is the angle bisector of angle MDK.

Proof:

To prove that DP is the angle bisector of angle MDK, we need to show that the two angles formed by DP with the sides MD and DK are equal.

Let's consider triangle MDK.

From the given information, we have DM = DK. This implies that triangle MDK is an isosceles triangle.

In an isosceles triangle, the angles opposite to the equal sides are also equal.

Therefore, angle MDK = angle MKD.

Now, let's consider triangle MDP.

From the given information, we have MP = KP.

Since MP = KP, the line segment DP is the perpendicular bisector of the base MK of triangle MDK.

In a triangle, the perpendicular bisector of the base bisects the angle opposite to the base.

Therefore, angle MDP = angle PDK.

Since angle MDK = angle MKD and angle MDP = angle PDK, we can conclude that DP is the angle bisector of angle MDK.

Hence, the line segment DP is the angle bisector of angle MDK.