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Example 6: Verify whether D is the midpoint of AG. A B C D E F G

Solution: From the given figure, we find that 0 1 2 3 4 5 6 7
AG = 7 units – 1 unit = 6 units, (since A is at 1 unit and G is at 7 units from 0)
AD = 4 units – 1 unit = 3 units (since A is at 1 unit and D is at 4 units from 0)
and DG = 7 units – 4 units = 3 units (since D is at 4 units and G is at 7 units from 0)

This means AD = DG and AG = AD + DG
AG
or AG = AD + AD = 2AD so AD = 2 .

Thus, D is the midpoint of AG .

maths fun
Dots and Box Game
Players: Two
Materials required: A4 Sheet, 2 Coloured pencils
Procedure:
(a) On a white A4 sheet, draw 9 dots in a 3 by 3 square.
(b) T wo players take turns drawing lines between dots on the grid. Two adjacent dots
can be joined with a horizontal or vertical line. Both players will use different
coloured pencils/markers
(c) The player who creates a box will get one extra turn.
(d) The player who completes the maximum number of boxes wins the game.
Example:
The following game on a 3 × 3 grid is won by Blue, who scores 3 against Red’s 1:

B B

R R B R

This game can also be played using a 4 by 4 square dot grid.

Practice Time 2B

1. Identify the shortest and the longest sides of the given polygon. Verify your answer by using a divider.
B
N
(a) (b)

A
L M
D C
2. If B is the midpoint of AC and C is the mid-point of BD , where A, B, C, and D lie on a straight line,
explain why AB = CD ?

35 Lines and Angles