Chapter 3 of 8

All 8 chapters
  1. 1Straight lines and parallel lines, readunderstood
  2. 2Polygons, readunderstood
  3. 3Right angles and turns, readunderstood
  4. 4Measuring angles in degrees, readunderstood
  5. 5Triangles and four sided shapes, readunderstood
  6. 6Lines of symmetry, readunderstood
  7. 7Solid shapes and nets, readunderstood
  8. 8Grids and directions, readunderstood

M2.5.3 Chapter 3

Right angles and turns

How can I tell if a corner is a right angle?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

  • You picked A. Read on. At the end, the chapter comes back to your guess.

  • You picked B. Read on. At the end, the chapter comes back to your guess.

  • You picked C. Read on. At the end, the chapter comes back to your guess.

By the end you can

  • Make a right angle tester by folding paper twice
  • Compare an angle with a right angle: smaller, equal or bigger
  • Find lines that meet at a right angle

An angle is how much one line turns away from another. Think of a door. The wider it opens, the bigger the angle.

A right angle is a square corner, like a book corner.

Draw it first

Fold a right angle tester

  1. A piece of paper. Step 1 shows the paper with a dashed line across it, labelled first fold. Step 2 shows the folded paper with a dashed line going up from the folded edge, labelled second fold. Step 3 shows the corner you made, marked with a small square, labelled right angle.first fold

    1 Fold any piece of paper once. The fold is a straight edge.

  2. A piece of paper. Step 1 shows the paper with a dashed line across it, labelled first fold. Step 2 shows the folded paper with a dashed line going up from the folded edge, labelled second fold. Step 3 shows the corner you made, marked with a small square, labelled right angle.second fold

    2 Fold it again. Make the folded edge lie exactly along itself.

  3. A piece of paper. Step 1 shows the paper with a dashed line across it, labelled first fold. Step 2 shows the folded paper with a dashed line going up from the folded edge, labelled second fold. Step 3 shows the corner you made, marked with a small square, labelled right angle.right angle

    3 Press it flat. The corner you made is a right angle.

This is your right angle tester. It works on any piece of paper.

Lay the tester in a corner. Is the corner smaller than the tester, equal to it, or bigger?

A corner smaller than a right angle is acute. A corner bigger than a right angle is obtuse.

Three angles. The first is smaller than a right angle, labelled acute. The second has a small square in it, labelled right angle. The third is bigger than a right angle, labelled obtuse.acuteright angleobtuse
Lay your tester on each corner. Acute is smaller. Obtuse is bigger.

Turns are angles too. A quarter turn is one right angle. A half turn is two. A full turn is four.

Two straight lines cross. They make four right angles, numbered 1, 2, 3 and 4. Angle 1 is marked with a small square.1234
All four angles are right angles. Four fill a full turn. Two fill a half turn.

See it three ways

With things

Face a wall. Turn a quarter turn to the right. You have turned one right angle.

As a picture

A right angle marked with a small square. The label says quarter turn.quarter turn

In symbols

2 quarter turns = 1 half turn. 4 quarter turns = 1 full turn.

Two lines that meet at a right angle are perpendicular.

Two pairs of crossing lines. The first pair meets at a right angle, marked with a small square, and is labelled perpendicular. The second pair crosses at a slant, with no square, and is labelled not perpendicular.perpendicularnot perpendicular
Perpendicular lines make a right angle. Check with your tester.

Try it

Make a tester and use it

You need: any piece of paper, things with corners, such as a book, a door and a window.

  1. Fold the paper once.
  2. Fold it again. Make the first fold lie along itself.
  3. Press the folds flat. The corner is your tester.
  4. Lay the tester in the corner of a book. Does it fit?
  5. Try a door, a window and a table. Say smaller, equal or bigger.

What you will see: The tester fits the corners of a book and a door. It does not fit a corner that is wider or narrower.

If you cannot try it, this is what happens.
The corner of a book, drawn as two lines that meet at a right angle. A folded paper tester, labelled tester, sits in the corner and fits exactly.tester
Two right angles. The left one has short lines, labelled short arms. The right one has long lines, labelled long arms. Both have a small square.short armslong arms
Both angles are right angles. Your tester fits both.

A wrong idea many people have

An angle with longer lines is a bigger angle.

Why it feels right: A picture with long lines looks bigger on the page.

The test that breaks it: Draw a right angle with short lines. Draw another with long lines. Lay your tester on both. It fits both.

What is true: The size of an angle is how much it turns. The length of the lines does not matter.

Key words

right angle
a square corner. It is a quarter turn.
acute
smaller than a right angle.
obtuse
bigger than a right angle, but smaller than a straight line.
perpendicular
lines that meet at a right angle.

Back to your guess

The answer is B: Fold paper twice to make a tester. Lay it in the corner.

A tester checks every corner the same way. Your eyes can be fooled. A ruler measures length, not the corner.

Check yourself

Try each one before you look. A wrong answer tells you where to go next.

  1. How do you make a right angle tester?

    Tap your answer.

    1. Yes, that is right. The second fold makes the folded edge lie along itself. That makes a square corner.

    2. Not this one. One fold makes a straight edge. It does not make a corner. Try another.

    3. Not this one. A torn corner can be any size. It may not be a right angle. Try another.

    See the answer

    Fold paper twice. Make the first fold lie along itself.

    The second fold makes the folded edge lie along itself. That makes a square corner.

    • If you chose B: One fold makes a straight edge. It does not make a corner.
    • If you chose C: A torn corner can be any size. It may not be a right angle.

  2. Compare this angle with a right angle. Is it smaller, equal or bigger?

    An angle with the letter a inside it. It is wider than a right angle.a
    Tap your answer.

    1. Not this one. Lay a tester on it. The angle is wider than the tester, so it is bigger. Try another.

    2. Not this one. A right angle is a square corner. This angle opens wider than that. Try another.

    3. Yes, that is right. The angle opens wider than a right angle. It is an obtuse angle.

    See the answer

    Bigger

    The angle opens wider than a right angle. It is an obtuse angle.

    • If you chose A: Lay a tester on it. The angle is wider than the tester, so it is bigger.
    • If you chose B: A right angle is a square corner. This angle opens wider than that.

  3. Ravi draws a right angle with lines 5 cm long. Mei draws one with lines 10 cm long. Whose angle is bigger?

    Tap your answer.

    1. Not this one. Long lines do not make a bigger angle. A tester fits both. Try another.

    2. Not this one. Both angles turn a quarter turn. The length of the lines does not change that. Try another.

    3. Yes, that is right. Both are right angles. The size of an angle is how much it turns.

    See the answer

    They are the same size

    Both are right angles. The size of an angle is how much it turns.

    • If you chose A: Long lines do not make a bigger angle. A tester fits both.
    • If you chose B: Both angles turn a quarter turn. The length of the lines does not change that.

  4. Mei turns a half turn. Then she turns a quarter turn. How many right angles has she turned in all?

    See the answer

    3 right angles

    A half turn is 2 right angles. A quarter turn is 1. 2 + 1 = 3.

  5. From an earlier chapter

    Which of these is a polygon?

    Tap your answer.

    1. Not this one. A circle has a curved edge. A polygon has only straight sides. Go to M2.5.2. Try another.

    2. Yes, that is right. A hexagon is flat and closed, and it has 6 straight sides.

    3. Not this one. A polygon must be closed. It has no gaps. Go to M2.5.2. Try another.

    See the answer

    A hexagon

    A hexagon is flat and closed, and it has 6 straight sides.

    • If you chose A: A circle has a curved edge. A polygon has only straight sides. Go to M2.5.2.
    • If you chose C: A polygon must be closed. It has no gaps. Go to M2.5.2.

  6. Find two pairs of perpendicular lines in your room. Check them with your tester.

    See the answer

    The two sides of a book corner. The edge of a door and the floor.

    In each pair the lines meet at a right angle. Your tester fits the corner.

  7. What is true of two perpendicular lines?

    Tap your answer.

    1. Yes, that is right. Perpendicular lines meet at a right angle. It does not matter which way the page is turned.

    2. Not this one. That describes parallel lines. Perpendicular lines meet at a right angle. Go to M2.5.1. Try another.

    3. Not this one. Turn the page and both lines turn. The corner is still a right angle, so they are still perpendicular. Try another.

    See the answer

    They meet at a right angle.

    Perpendicular lines meet at a right angle. It does not matter which way the page is turned.

    • If you chose B: That describes parallel lines. Perpendicular lines meet at a right angle. Go to M2.5.1.
    • If you chose C: Turn the page and both lines turn. The corner is still a right angle, so they are still perpendicular.

  8. Hana lays her tester in a corner. It fits inside, with space left beside it. Is the corner smaller, equal or bigger?

    Two lines meet at a corner. The corner is labelled corner. A square tester, labelled tester, sits inside it with its own corner on the corner. There is a gap between the tester and the upper line.cornertester
    Tap your answer.

    1. Not this one. The tester fits inside with room to spare. So the corner opens wider than the tester. Try another.

    2. Yes, that is right. The corner opens wider than the tester. A corner wider than a right angle is obtuse.

    3. Not this one. If it were equal, the tester would touch both lines. Here it does not. Try another.

    See the answer

    Bigger than a right angle

    The corner opens wider than the tester. A corner wider than a right angle is obtuse.

    • If you chose A: The tester fits inside with room to spare. So the corner opens wider than the tester.
    • If you chose C: If it were equal, the tester would touch both lines. Here it does not.

Keep it

Copy this into your exercise book.

Fold paper twice to make a right angle tester. Acute is smaller than a right angle. Obtuse is bigger. The size of an angle is how much it turns.

Draw: A right angle with a small square. Beside it, an acute angle and an obtuse angle.

Reading with a child? A short page for the adult: what this chapter teaches and three questions to ask.

No internet tomorrow? Save the whole book as one file (773 KB). It opens on any phone.