A line to the corner across
Show on a big screenThe line that cuts a tile into two triangles has a name. What is it?
- A quadrilateral, corners A, B, C, D.
- A and B are neighbours — AB is a side.
- A and C are not neighbours — AC is a diagonal.
- Two diagonals in all: AC and BD.
It is called a diagonal. Two corners are neighbours when one side joins them.
Rule: A diagonal joins two corners that are not neighbours. A quadrilateral has four corners and exactly two diagonals.
Take a shape with n corners. From one corner, you cannot draw a diagonal to that corner itself. You cannot draw one to either neighbour. So n − 3 corners are left to reach. Doing this from every corner counts each diagonal twice. So divide by 2. This gives every count below.
| Corners | Sides | Diagonals | n × (n − 3) ÷ 2 |
|---|---|---|---|
| 4 | 4 | 2 | 4 × 1 ÷ 2 = 2 |
| 5 | 5 | 5 | 5 × 2 ÷ 2 = 5 |
| 6 | 6 | 9 | 6 × 3 ÷ 2 = 9 |
Watch out!
A quadrilateral does not have four diagonals, one per corner. The line from A and the line from C are one line. Counting it from both ends counts it twice. Halving gives the real count: two.
Tap Add a corner. Count the lines across the middle.
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Try the lab to finish this lesson.