IMOClass 4 › Geometry

Geometry

Angles & Lines

A right angle measures 90°, an acute angle is less than 90°, and an obtuse angle is more than 90° but less than 180°.

Parallel lines always stay the same distance apart and never meet, like railway tracks. Perpendicular lines cross each other making a right angle.

Example 1: What kind of angle is 45°?
Less than 90°, so it is an acute angle.
Example 2: What kind of lines are railway tracks?
Parallel lines — they never meet.
Quick recap
  • Right = 90°, acute < 90°, obtuse > 90°.
  • Parallel lines never meet; perpendicular lines meet at a right angle.
✓ Quick check
A right angle measures ___ degrees.
A right angle is exactly 90°.
An angle of 120° is ___ ?
120° is more than 90°, so it is obtuse.

Parts of a Circle

The centre is the middle of a circle. The radius is the distance from the centre to the edge. The diameter goes right across through the centre and equals two radii (diameter = 2 × radius). A chord joins any two points on the circle, and the longest chord is the diameter.

Example 1: A circle has a radius of 5 cm. What is its diameter?
Diameter = 2 × 5 = 10 cm.
Example 2: What is the longest chord of a circle called?
The diameter.
Quick recap
  • Radius = centre to edge; diameter = across through the centre.
  • Diameter = 2 × radius; the longest chord is the diameter.
✓ Quick check
If the radius is 7 cm, the diameter is ___ ?
Diameter = 2 × 7 = 14 cm.
The line from the centre to the edge of a circle is the ___ ?
That line is the radius.

Symmetry & Nets

A shape has line symmetry if a line splits it into two matching halves. A square has 4 lines of symmetry, a rectangle has 2, and a circle has many.

A net is a flat shape that folds into a solid. The net of a cube has 6 square faces, and the net of a cuboid has 6 rectangular faces.

Example 1: How many lines of symmetry does a rectangle have?
2 lines of symmetry.
Example 2: How many squares are there in the net of a cube?
6 squares, one for each face.
Quick recap
  • Square has 4 lines of symmetry; rectangle has 2.
  • A net folds into a solid; a cube's net has 6 squares.
✓ Quick check
How many lines of symmetry does a square have?
A square has 4 lines of symmetry.
How many faces does the net of a cuboid have?
A cuboid has 6 faces, so its net has 6 rectangles.
Ready to test this chapter?
Take the Chapter Test →