Question

В равнобедренном треугольнике DFE на боковых сторонах DF и EF соответственно отметили точки M и K так что FM=FK; Докажите что угол DME=DKE.

Answer 1

Ответ:

Углы при основании триугольников равны, DE общая сторона, стороны равны. отсюда треугольники равны.

Answer 2

Given Information:

We are given a triangle DFE, where DF and EF are the two equal sides of the triangle. Points M and K are marked on the sides DF and EF respectively, such that FM = FK.

To Prove:

We need to prove that angle DME is equal to angle DKE.

Proof:

To prove that angle DME is equal to angle DKE, we can use the fact that the triangle DFE is an isosceles triangle.

Since DF and EF are equal sides, we have: - DM = EM (as M is the midpoint of DF) - EK = FK (as K is the midpoint of EF)

Now, let's consider the triangles DME and DKE.

In triangle DME: - DM = EM (as mentioned above) - Angle DME = Angle DME (common angle)

In triangle DKE: - EK = FK (as mentioned above) - Angle DKE = Angle DKE (common angle)

Since DM = EM and EK = FK, and the angles DME and DKE are common angles, we can conclude that triangle DME is congruent to triangle DKE by the Side-Angle-Side (SAS) congruence criterion.

By the congruence of triangles DME and DKE, we can conclude that angle DME is equal to angle DKE.

Therefore, we have proved that angle DME is equal to angle DKE in the given triangle DFE.

Note: The proof assumes that the given triangle DFE is isosceles and that points M and K are the midpoints of the sides DF and EF respectively. If there are any additional conditions or constraints given in the problem, please provide them for a more specific proof.