Plane Figures: Oblique and Perpendicular Lines
- Box of sticks
- Measuring angle
- Take two pairs of sticks with holes along the length and connect each pair with a brad at the center.
- Let's see how two straight lines can meet.
- Two straight lines can meet this way X or (rotate the second pair from an overlapping position, through the position shown so that the child may see that they are equal and then on to a perpendicular position) two straight lines can meet this way + (Note: each pair started form a horizontal position).
- Invite the child to measure the four angles of the first pair to see if they are right angles.
- None are right angles. In the second pair, all are right angles.
- When two straight lines meet and do not form angles that are right angles, the tow straight lines are oblique to each other.
- Review the meaning of oblique (deviated, slanting, not right).
- When two straight lines meet and form all right angles they are perpendicular to each other (perpendicular: Latin perpendicularis < perpendiculum, a plumb line < per, through and pendere, to hang).
- This perpendicular line hangs and goes through the other.
- Note: the Old English word for plumb line is perpendicle.
- Three period lesson with child constructing them.
Control Of Error
Points Of Interest
1. Place a pair of overlapping sticks horizontally with the measuring angle positioned at the vertex. Ask the child to identify how the lines are in relation to one another as the top stick rotates ... oblique, oblique... perpendicular, oblique .... as they overlap again - silence) .... oblique ... etc.
2. The child is asked to take three pairs of sticks and unite them with brads in this way:
1st pair - both have hole along the length; united at the center
2nd pair - one has holes, the other is normal; united at the center of the one with holes
3rd pair - both have only end holes; united at one end.
The sticks are lain overlapping in horizontal positions. Using the measuring angle the child makes the first pair perpendicular and counts the right angles formed (4). The number is written on a piece of paper and is placed by the pair. The same procedure is followed for the second and third pairs. When two lines meet and are perpendicular to each other, they create four right angles, or two right angles or one right angle. Invite the child to try o arrange two perpendicular lines that create three right angles. It is not possible.
The first pair are two straight lines; the second are a line and a ray; the third are two rays.
3. With one pair of sticks with holes joined at the center and placed horizontally on the board, the child is asked to make the two line perpendicular, checking with the measuring angle. These lines are perpendicular. The teacher turns the whole thing 450 and measures the angles to check. How are these lines in relation to each other? Still perpendicular. Before the lines were horizontal and vertical, now both are in an oblique position. Do the same with the second and third pairs from the previous exercises. With the measuring angle, show that right angles are always formed, regardless of the position of the lines. Therefore all of these lines are still perpendicular to each other because the amplitude of the angle didn't change.