Question

Отрезки МЕ и РК точкой D делятся пополам. Докажите,что kmD=PED решить

Answer 1

Как я поняла, предыдущее решение не относится к заданному вопросу...

Эти треугольники равны т.к. у них стороны РД=ДК, МД=ДЕ, и угол МДК=углу РДЕ.

Answer 2

Там два угла равны как вертикальные, а стороны равны по жизни, потому что пополам. И получаем равенство MED и PKD по двум сторонам и углу. А тогда получается, что MEPK - параллелограмм, потому что у него противоположные стороны равны и параллельны (что параллельны - доказывается из равенства внутренних накрест лежащих).

Answer 3

Proof that kmD = PED

To prove that kmD = PED, we need to show that the segments ME and RK, which intersect at point D, divide each other into equal halves.

Let's consider the given diagram:

          M
          |
          E
          |
          D
         / \
        /   \
       /     \
      /       \
     /         \
    /           \
   /             \
  /               \
 P-----------------D
  \               /
   \             /
    \           /
     \         /
      \       /
       \     /
        \   /
         \ /
          K

We are given that the segments ME and RK divide each other into equal halves. In other words, MD = DE and KD = DR.

To prove that kmD = PED, we need to show that the angles kmD and PED are equal.

Let's consider the triangles kmD and PED:

Triangle kmD: - Side MD is equal to side DE (given) - Side KD is equal to side DR (given) - Angle kmD is common to both triangles

Triangle PED: - Side PD is common to both triangles - Side ED is equal to side DR (given) - Side PE is equal to side MD (given)

By the Side-Angle-Side (SAS) congruence criterion, if two sides and the included angle of one triangle are equal to the corresponding sides and included angle of another triangle, then the two triangles are congruent.

Since the triangles kmD and PED have two sides and the included angle equal, they are congruent.

Therefore, the angles kmD and PED are equal.

Hence, we have proved that kmD = PED.