Solids, angles and quadrilaterals · Usually met around P2
Line segments and quadrilaterals
4 points: 3 + 2 + 1 = 6 segments.
How to do it
Method
4 points: 3 + 2 + 1 = 6 segments
AB's opposite side is CD; its neighbours are BC and AD
Another way
List them
AB, AC, AD, BC, BD, CD
In full
A line segment is a piece of a straight line with two endpoints; of all the ways between two points, the segment is the shortest. To count segments, start from each point and count to its right: with 4 points A, B, C, D on a line, A starts 3, B 2 and C 1, 3 + 2 + 1 = 6. A quadrilateral has 4 straight sides and 4 angles. In quadrilateral ABCD, two sides facing each other with no endpoint in common are opposite sides, like AB and CD; sides sharing an endpoint are adjacent, like AB and BC. Or list every segment: AB, AC, AD, BC, BD, CD.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
There are 5 points on the line. How many segments have two of them as endpoints?
Show the answer and working
Answer: 10 segments
Count to the right from each point and add: 10 in all.
Example 2
In quadrilateral ABCD, which side is opposite AB?
- A. AC
- B. BC
- C. AD
- D. CD
Choose the right answer
Show the answer and working
Answer: D. CD
Going round A, B, C, D, the side sharing no endpoint with AB is CD.
Example 3
5 points lie on a line, each 8 cm from the next. How long is the longest segment?
Show the answer and working
Answer: 32 cm
The longest runs from the first point to the last, across 4 gaps: 32 cm.
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