Angles & Geometry

Angle types, triangle properties, quadrilaterals and symmetry

Explanation

Types of Angles

  • Acute: less than 90°
  • Right: exactly 90°
  • Obtuse: between 90° and 180°
  • Straight: exactly 180°
  • Reflex: between 180° and 360°

Angle Relationships

RuleMeaning
Complementary anglesSum to 90°
Supplementary anglesSum to 180°
Angles at a pointSum to 360°
Vertically oppositeEqual (formed by crossing lines)
Corresponding anglesEqual (parallel lines, same side)
Alternate anglesEqual (parallel lines, opposite sides)
Co-interior anglesSum to 180° (parallel lines, same side)

Triangles

Angles in any triangle sum to 180°.

  • Equilateral: all sides and angles equal (60° each)
  • Isosceles: two equal sides and two equal base angles
  • Scalene: no equal sides or angles
  • Right-angled: one 90° angle

Quadrilaterals & Polygons

Angles in any quadrilateral sum to 360°.

Key shapes: square, rectangle, rhombus, parallelogram, trapezium, kite

Interior Angles of Polygons

Sum of interior angles = (n − 2) × 180° where n = number of sides

Example: Pentagon (5 sides): (5−2) × 180 = 540°
Each angle in a regular pentagon = 540° ÷ 5 = 108°

Pythagoras & Key Tips

In a right-angled triangle: a² + b² = c² where c is the hypotenuse (longest side).

Example: Find the hypotenuse if the other sides are 3 and 4.
c² = 3² + 4² = 9 + 16 = 25 → c = 5

Key Tips

  • Always give a reason for each angle found in geometry proofs
  • Mark equal angles and sides on your diagram as you work
  • Common Pythagorean triples: (3,4,5), (5,12,13), (8,15,17)

Sample Practice Questions

  1. A right-angled triangle has legs 3 cm and 4 cm. What is the length of the hypotenuse?

    • 3.5 cm
    • 5 cm
    • 7 cm
    • 25 cm
    Show answer

    Answer: 5 cm

  2. How many sides does a hexagon have?

    • 5
    • 6
    • 7
    • 8
    Show answer

    Answer: 6

  3. What is the sum of the interior angles of a triangle?

    • 90°
    • 180°
    • 270°
    • 360°
    Show answer

    Answer: 180°

  4. What is the exterior angle of a regular octagon?

    • 30°
    • 40°
    • 45°
    • 60°
    Show answer

    Answer: 45°

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Practice Questions

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Frequently Asked Questions

What does Angles & Geometry cover in the Selective Entry exam?

Angle types, triangle properties, quadrilaterals and symmetry.

How can I practise Angles & Geometry questions for the Victorian Selective Entry test?

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