Question

Give a paragraph for each to explain.

1. Allie says that  are parallel because they do not intersect. How do you respond?

2. Rajesh named the line below as . How do you respond?

3. A student says that  because  starts at A and ends at B and  starts at B and ends at A. How do you respond?

4. Henry claims that a line segment has a finite number of points because it has two endpoints. How do you respond?

5. A student claims that if any two planes that do not intersect are parallel, then any two lines that do not intersect should also be parallel. How do you respond?

6. A student says that it is actually impossible to measure an angle, since each angle is the union of two rays that extend indefinitely and therefore continue forever. What is your response?

7. Maggie claims that to make the measure of an angle greater, you just extend the rays. How do you respond?

8. A student says that there can be only 360 different rays emanating from a point since there are only  in a circle. How do you respond?

9. A student asks why an angle is not defined as the union of two half-lines and a common point. How do you respond?

Answer 1

Q.No.1:

ANSWER:

The parallel lines never intersect each other because the Distance between them are equal till infinity so If they will intersect then we will call it intersecting lines. It is the property of parallel lines that they did not Intersect with each other and we can’t change this property.

Q.No.2 & Q.No.3:

ANSWER:

Starts at A and ends at B and  starts at B and ends at A, Rajesh named this as a line. But this ins not correct.

Because, A line goes without end in both directions. Both ends of a line can go to infinity. A line has no end points. The length of a line cannot be measured. A line has no definite length.

But he can name it as a line segment. Because A line segment has two endpoints. A line segment is a straight line that connects two points. It is the shortest path between the two points. A line segment has definite length. Its length can be measured. There is no arrow on any end. It starts from one point and ends at another point. This is called a line segment. A section of a line is a line segment.

Q.No.4:

ANSWER:

No this statement made Henry is not correct. Let us try to explain it as given below.

Let's assume that your end points are A(0,0) and B(1,0).

Try to find a point in between them. Ok you found C(0.4,0).

Now try finding another point. Will you ever NOT be able to find another point? No, because there are infinite numbers between 0 and 1 (just think of decimals).

In the same way there are infinite points in a line segment.

-------------------------------- thanks