Question

В равнобедренном треугольнике КРН с основанием КН проведена медиана РД Точка А середина стороны РК Точка В середина стороны РН . докажите равенство треугольников РДА и РДВ​.

Answer 1

Ответ:

решение на фото...........

Answer 2

To prove the congruence of triangles RDA and RDV, we can use the property that the medians of a triangle divide each other into segments of the same ratio. Let's go through the proof step by step:

Given Information:

- Triangle KRN is an isosceles triangle with base KN. - Median RD is drawn from vertex R, intersecting base KN at point D. - Point A is the midpoint of side RK. - Point B is the midpoint of side RN.

Proof:

1. Since point A is the midpoint of side RK, we can conclude that AD is half the length of RK. 2. Similarly, since point B is the midpoint of side RN, we can conclude that BD is half the length of RN. 3. As the medians of a triangle divide each other into segments of the same ratio, we can say that AD:DR = BD:DV. 4. Since AD is half the length of RK and BD is half the length of RN, we can substitute these values into the ratio: (1/2)RK:DR = (1/2)RN:DV. 5. Simplifying the ratio, we get RK:DR = RN:DV. 6. Since triangle KRN is an isosceles triangle, RK = RN. 7. Therefore, the ratio RK:DR = RN:DV can be rewritten as RK:DR = RK:DV. 8. By the transitive property of equality, we can conclude that DR = DV. 9. Since DR = DV, and DA = DB (both are medians of triangle RDA and RDV), we can conclude that triangle RDA is congruent to triangle RDV by the Side-Side-Side (SSS) congruence criterion.

Therefore, we have proved that triangles RDA and RDV are congruent.