Question

В параллелограмме КMNO диагонали пересекаются в точке D.Докажите ,что треугольник КDM равен треугольнику NDO

Answer 1

1) KM=NO они противоположные стороны
2)угол 1 =2 и угол 3=4 накрест лежащие углы ровны с секущими KN и MO из этого исходит что кдо =ндо

Answer 2

Parallelogram KMNO and Triangle KDM and NDO

To prove that triangle KDM is equal to triangle NDO in parallelogram KMNO, we can use the concept of opposite sides and angles in a parallelogram.

In a parallelogram, opposite sides are equal in length and opposite angles are equal in measure. Let's break down the proof step by step:

1. Given: Parallelogram KMNO with diagonals intersecting at point D.

2. To prove: Triangle KDM is equal to triangle NDO.

3. Proof:

- Since KMNO is a parallelogram, we know that KM is parallel to NO and KN is parallel to MO.

- In a parallelogram, opposite sides are equal in length. Therefore, KM = NO and KN = MO.

- Now, let's consider triangle KDM and triangle NDO.

- In triangle KDM, KD is a side and DM is another side.

- In triangle NDO, ND is a side and DO is another side.

- Since KM = NO and KN = MO, we can conclude that KMNO is a rectangle.

- In a rectangle, diagonals are equal in length and bisect each other. Therefore, KD = DO and DM = ND.

- Now, we have KD = DO and DM = ND, which means that triangle KDM is congruent to triangle NDO by the Side-Side-Side (SSS) congruence criterion.

- Therefore, triangle KDM is equal to triangle NDO.

4. Conclusion: We have proved that triangle KDM is equal to triangle NDO in parallelogram KMNO.

Please let me know if you have any further questions!