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Mathematics · Grades 5–9

Geometry: justify, do not just measure

A drawing may not be to scale. Apply the stated properties.

Make a worksheet

Understand the idea

Use defining properties

A drawing may not be to scale. Apply the stated properties.

Separate measures

Perimeter measures boundary length; area measures surface coverage.

State assumptions

Angle rules here use ordinary plane Euclidean geometry.

Worked examples

Two angles in a triangle are 48° and 67°. Find the third angle in degrees.

180 − 48 − 67 = 65.

65

Which statement is true for every square?

These properties define a square in plane geometry.

It has four equal sides and four right angles.

Try it yourself

  1. A rectangle has perimeter 30 cm and length 9 cm. Find its width in cm.

  2. Can two rectangles have the same perimeter but different areas? Give an example.

  3. An angle of 135° is

    1. reflex
    2. obtuse
    3. right
    4. acute

  4. A straight angle is split into angles in the ratio 2:3. Find the smaller angle in degrees.

Answers and marking notes

Answers and marking notes
  1. 6

    2(9 + w) = 30, so 9 + w = 15.

  2. Yes. A 1 by 5 rectangle and a 2 by 4 rectangle both have perimeter 12, but areas 5 and 8.

    Accept another checked counterexample with consistent units.

  3. obtuse

    It is greater than 90° but less than 180°.

  4. 72

    180/5 = 36 per part; 2 × 36 = 72.

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