Question

F (1:1) H (6:1) S (7:4) K (2:4) доказать что это параллелограм

Answer 1

Нарисуй и посмотри. Почитай что такое параллелограмм ,если знаешь то еще лучше.

Answer 2

Given Information

We are given the following points: F(1,1), H(6,1), S(7,4), and K(2,4). We need to prove that these points form a parallelogram.

Understanding Parallelograms

A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length. To prove that a quadrilateral is a parallelogram, we can use different methods, such as showing that opposite sides are parallel or that opposite sides are equal in length.

Proving that FHSK is a Parallelogram

To prove that FHSK is a parallelogram, we can show that opposite sides are parallel or that opposite sides are equal in length.

Let's consider the line segments formed by the given points: - Line segment FH: This is formed by points F(1,1) and H(6,1). - Line segment SK: This is formed by points S(7,4) and K(2,4).

To show that FH and SK are parallel, we can compare their slopes. If the slopes are equal, the lines are parallel.

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula: slope = (y2 - y1) / (x2 - x1)

Let's calculate the slopes of FH and SK:

- Slope of FH: - (y2 - y1) = (1 - 1) = 0 - (x2 - x1) = (6 - 1) = 5 - slope = 0 / 5 = 0

- Slope of SK: - (y2 - y1) = (4 - 4) = 0 - (x2 - x1) = (2 - 7) = -5 - slope = 0 / -5 = 0

Since the slopes of FH and SK are both 0, the lines are parallel.

Therefore, we have shown that FH and SK are parallel, which means that FHSK is a parallelogram.

Conclusion

We have proven that the given points F(1,1), H(6,1), S(7,4), and K(2,4) form a parallelogram. The opposite sides FH and SK are parallel, satisfying the definition of a parallelogram.