Solids, angles and quadrilaterals · Usually met around P2
Right angles and perpendicular lines
The perpendicular segment is the shortest.
How to do it
Method
The perpendicular segment is the shortest
PA 5, PB 4, PC 6: PB is perpendicular, the shortest
Another way
Fold it
Fold the line onto itself: the crease is perpendicular
In full
Two straight lines that cross at a right angle are perpendicular; all four angles where they cross are right angles. Check with a set square: one edge along one line, and see if the other line runs along its other edge. From a point off a line you can draw many segments to the line; the one perpendicular to it is the shortest, and every slanting one is longer. The distance from a point to a line is the length of that perpendicular segment. Or fold paper so the line lies on itself: the fold is perpendicular to it.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
The two lines in the picture are perpendicular.
True or false?
Show the answer and working
Answer: False
Check the angle where they cross with a set square: only a right angle means perpendicular.
Example 2
How many pairs of neighbouring sides of this shape are perpendicular?
Show the answer and working
Answer: 0 pairs
Perpendicular neighbours make a right angle where they meet: count the right angles, 0.
Example 3
Four segments run from point P to the line. Which is the shortest?
- A. PB
- B. PC
- C. PD
- D. PA
Choose the right answer
Show the answer and working
Answer: D. PA
The segment perpendicular to the line is the shortest.
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