Two lines, four corners
Where two lines meet, how many angles are there?
A page, two lines
Your notebook page is a plane surface. So are a table top and a blackboard. Draw two lines on it so that they cross each other.
How many angles do the two lines make where they cross?
What this lesson covers
The idea
When a pair of lines on a plane surface meet each other at a point, the lines intersect each other, and four angles are formed where they meet.
A page, two lines
Your notebook page is a plane surface. So are a table top and a blackboard. Draw two lines on it so that they cross each other.
How many angles do the two lines make where they cross?
- 2 angles
- 4 angles
- 8 angles
Count the angles
The two lines meet at the point O. Count the angles they make.
Lines that meet
When a pair of lines on a plane surface meet each other at a point, we say that the lines intersect each other.
Where they meet, four angles are formed. Turn the line anywhere and it is still four.
A line goes on and on at both ends. So two lines whose drawn parts do not touch still intersect, if they would meet when you extend them.
When a pair of lines on a plane surface meet each other at a point, the lines intersect each other, and four angles are formed where they meet.
Notes
When a pair of lines on a plane surface meet each other at a point, the lines intersect each other, and four angles are formed where they meet.
Check yourself
The drawn parts of lines *p* and *q* do not touch. But they lean towards each other. Do the lines intersect?
Two lines intersect. One of the angles where they meet is shaded. How many other angles are formed there?
Answer: 3
Two intersecting lines make 4 angles. One is shaded, so 4 − 1 = 3 are the others.
Which pair of lines intersect?
Two lines cross at a very small tilt, so one angle is a thin sliver. How many angles do they make at O?
Answer: 4
Even a thin sliver is an angle. There are 4 angles at O: two thin ones and two wide ones.
- No. The drawn parts do not touch.. The drawn part is only a piece of a line. A line goes on at both ends, and these two meet when extended.
- Yes. A line has no end, so if we extend them they meet. — correct. Yes! Extend them to the right and they meet at one point.
- We cannot tell without drawing more.. We can tell: they lean towards each other, so extending them makes them meet.
- Two roads that cross at a crossroads — correct. Yes! The roads meet at one point, and four corners form there.
- The top edge and the bottom edge of a blackboard. These run side by side and never meet, so they do not intersect.
- The two long edges of a ruler. These run side by side and never meet, so they do not intersect.