Question

DE=DK CE=CK. Докажите,что луч CD-биссектриса углаECK

Answer 1

Треугольник СДЕ = треугольнику СДК (по третьему признаку СД -общая, ДЕ=ДК и СЕ=СК - по условию). В равных треугольниках против равных сторон лежат равные углы. Значит угол ДСЕ=углу ДСК, отсюда следует, что СД - биссектриса угла ЕСК

Answer 2

Потому что квадрат ECKD

Answer 3

Proof that CD is the bisector of angle ECK

To prove that CD is the bisector of angle ECK, we need to show that it divides the angle ECK into two equal angles.

Given: DE = DK and CE = CK

We can start by drawing a diagram to visualize the given information. Let's label the points as shown below:

          C
         / \
        /   \
       /     \
      /       \
     /         \
    /           \
   D-------------K
        E

Now, let's consider triangle ECK. We know that DE = DK and CE = CK.

By the Side-Angle-Side (SAS) congruence criterion, we can conclude that triangle DEK is congruent to triangle CEK.

Since congruent triangles have equal corresponding angles, we can say that angle DEK is equal to angle CEK.

Now, let's draw a line segment CD to connect points C and D.

          C
         / \
        /   \
       /     \
      /       \
     /         \
    /           \
   D-------------K
        E

Since angle DEK is equal to angle CEK, and CD is a common side, we can conclude that CD is the bisector of angle ECK.

Therefore, we have proven that CD is the bisector of angle ECK.

Note: The proof provided above is based on the given information and the assumption that DE = DK and CE = CK. If there are any additional constraints or information, please let me know, and I'll be happy to assist you further.