Discover Mathematics P4: Term 2, Unit 12, Lessons 6–10
GoalRecognise a right angle, test for it with the corner of a paper, and find right angles in shapes and objects.
New words
angle · the opening between two rays that start at the same endpointvertex of an angle · the common endpoint where the two rays meetright angle · a square corner; a quarter of a full turn
Explanation
An angle is made by two rays that start at the same point. The point is the vertex of the angle, and the rays are its arms. The size of an angle tells how wide the opening is. The most important angle is the right angle. It is a square corner, like the corner of a page, a door or a tile. A right angle is a quarter of a full turn and measures 90° (ninety degrees; we will learn how to measure degrees soon). We mark a right angle with a small square at the vertex. To test an angle, put the corner of a sheet of paper on its vertex and one arm along a side of the paper. If the other arm fits the other side of the paper exactly, the angle is a right angle. A square and a rectangle have four right angles each.
Worked examples
Two rays that start at B make angle ABC. B is the vertex, and BA and BC are the arms. The arc inside shows which opening we mean. Here the arms open less than a square corner.
Test three angles with the corner of a paper. Angle A is wider than the paper corner, angle B fits it exactly and angle C is narrower. Only angle B is a right angle.
Right angles in a shape. In triangle ABC the small square at C shows a right angle. This triangle has one right angle. A rectangle has four, one at each corner. A set square from your geometry box has one right angle.
Class activity
Right angle hunt. Make a right-angle tester by folding a piece of paper twice (the second fold along the first fold). Walk round your home and find five right angles: for example the corners of a book, a window, a box and a tile. Draw each one and mark the right angle with a small square. Is there anything that looks like a right angle but is not?
Practice
1
Which angle in the picture is a right angle: A, B or C?
Angle B. A is narrower than a square corner and C is wider.
2
How many right angles does a square have?
4, one at each corner.
3
Name three objects that have right angles.
For example: a door, a book, a floor tile, a window.
4
At what time do the hands of a clock make a right angle: 3 o’clock or 6 o’clock?
3 o’clock. At 6 o’clock the hands make a straight line.
5
Karim says a triangle can have two right angles. Is he right?
No. If two angles were right angles, the two sides would be parallel and would never meet, so the triangle could not close.
