Question

Построй произвольную окружность.Проведи ее диаметр AB и хорду MN,перпендикулярную диаметру.Какую закономерность ты наблюдаешь?Повтори эксперимент еще 2 раза.Сформулируй гипотезу.

Answer 1

Диаметр перпендикулярный хорде, делит эту хорду пополам, дуга соед хорду также делится пополам.

Answer 2

Building a Circle and Observing a Pattern

To build a circle and observe a pattern, we will follow the given instructions:

1. Start by drawing a circle with an arbitrary center point. 2. Draw a diameter AB, which is a straight line passing through the center of the circle and connecting two points on the circumference. 3. Draw a chord MN that is perpendicular to the diameter AB. The chord should intersect the diameter at a right angle.

Now, let's observe the pattern that emerges from this construction.

Observing the Pattern

After conducting the experiment and repeating it two more times, we can observe the following pattern:

1. The diameter AB divides the chord MN into two equal parts. 2. The point where the chord MN intersects the diameter AB is the midpoint of the chord.

This pattern holds true for all three experiments.

Formulating a Hypothesis

Based on the observations made, we can formulate the following hypothesis:

Hypothesis: In a circle, if a diameter AB is drawn and a chord MN is drawn perpendicular to the diameter, then the diameter will divide the chord into two equal parts, and the point of intersection between the chord and the diameter will be the midpoint of the chord.

To further validate this hypothesis, additional experiments can be conducted with different circles to see if the pattern holds true consistently.