Question

В равнобедренном треугольнике АВС АВ = СВ. Точка D делит основание АС пополам. Точка К - внутренняя точка отрезка ВD. Докажите, что АК = СК.

Answer 1

Объяснение:

тк BD делит основание пополам в равнобедренном треугольнике, то она высота (по теории)

По теории она также и срединнный перпендикуляр

Из теории следует, что от любой точки следующая перпендикулярное расстояние до точек равно

Answer 2

Given Information:

We are given a triangle ABC, where AB = BC. Point D divides the base AC in half, and point K is an internal point on segment BD. We need to prove that AK = CK.

Proof:

To prove that AK = CK, we can use the fact that the triangle ABC is isosceles (given that AB = BC). Let's consider the following steps:

1. Since AB = BC, triangle ABC is an isosceles triangle. 2. In an isosceles triangle, the angles opposite the equal sides are also equal. 3. Therefore, angle ABC = angle BAC. 4. Since point D divides the base AC in half, AD = DC. 5. Now, let's consider triangle ABD and triangle CBD. 6. In triangle ABD, AD = DC (from step 4) and AB = BC (given). 7. By the Side-Angle-Side (SAS) congruence criterion, triangle ABD is congruent to triangle CBD. 8. Therefore, angle ABD = angle CBD. 9. Since angle ABC = angle BAC (from step 3) and angle ABD = angle CBD (from step 8), we can conclude that angle ABK = angle CBK. 10. Since angles ABK and CBK are equal, the triangles ABK and CBK are similar. 11. In similar triangles, the corresponding sides are proportional. 12. Therefore, AK/CK = AB/CB = 1 (since AB = BC). 13. This implies that AK = CK.

Hence, we have proved that AK = CK in the given triangle ABC.