Types of angles
■■ Types of angles
Acute (0–90°) Right (90°) Obtuse (90–180°)
Straight (180°) Reflex (180–360°) Revolution (360°)
■■ Special pairs of angles at a point include:
• Complementary angles (sum to 90°) a + b = 90
• Supplementary angles (sum to 180°) a + d = 180
• Vertically opposite angles (equal) a = c
■■ Angles in a revolution sum to 360°.
■■ Two lines are perpendicular if they intersect at right angles (90°).
■■ 8 point compass bearing
• Bearings are usually measured clockwise from north.
■■ A transversal is a line cutting at least two other lines.
■■ Pairs of angles formed by transversals can be:
• corresponding (in corresponding positions)
• alternate (on opposite sides of the transversal and inside the other two lines)
• Co-interior (on the same side of the transversal and inside the other two lines).
■■ Lines are parallel if they do not intersect.
• Parallel lines are marked with the same number of arrows. or ■■ If two parallel lines are cut by a transversal
• the corresponding angles are equal (4 pairs)
• the alternate angles are equal (2 pairs)
• the co-interior angles are supplementary
(sum to 180°) (2 pairs).
A triangle with vertices A, B and C is written Δ ABC.
■■ The minimal conditions for a unique triangle are:
• SSS (3 sides)
• SAS (2 sides and the included angle)
• ASA (2 angles and the side between)Key ideas
• AAS (2 angles and a side not between)
• RHS (a right angle, the hypotenuse and another side)
Quadrilaterals can be convex or non-convex.
• Convex quadrilaterals have all vertices pointing outwards.
• Non-convex (or concave) quadrilaterals have one vertex pointing inwards.
Convex
All interior angles less than 180°
Non-convex
One reflex interior angle
■■ Special quadrilaterals
Square Rectangle Rhombus
Parallelogram Kite Trapezium
■■ The angle sum of any quadrilateral is 360.
Polygons can be convex or non-convex.
• Convex polygons have all vertices pointing outwards.
• Non-convex (or concave) polygons have at least one vertex pointing inwards.
Acute (0–90°) Right (90°) Obtuse (90–180°)
Straight (180°) Reflex (180–360°) Revolution (360°)
■■ Special pairs of angles at a point include:
• Complementary angles (sum to 90°) a + b = 90
• Supplementary angles (sum to 180°) a + d = 180
• Vertically opposite angles (equal) a = c
■■ Angles in a revolution sum to 360°.
■■ Two lines are perpendicular if they intersect at right angles (90°).
■■ 8 point compass bearing
• Bearings are usually measured clockwise from north.
■■ A transversal is a line cutting at least two other lines.
■■ Pairs of angles formed by transversals can be:
• corresponding (in corresponding positions)
• alternate (on opposite sides of the transversal and inside the other two lines)
• Co-interior (on the same side of the transversal and inside the other two lines).
■■ Lines are parallel if they do not intersect.
• Parallel lines are marked with the same number of arrows. or ■■ If two parallel lines are cut by a transversal
• the corresponding angles are equal (4 pairs)
• the alternate angles are equal (2 pairs)
• the co-interior angles are supplementary
(sum to 180°) (2 pairs).
A triangle with vertices A, B and C is written Δ ABC.
■■ The minimal conditions for a unique triangle are:
• SSS (3 sides)
• SAS (2 sides and the included angle)
• ASA (2 angles and the side between)Key ideas
• AAS (2 angles and a side not between)
• RHS (a right angle, the hypotenuse and another side)
Quadrilaterals can be convex or non-convex.
• Convex quadrilaterals have all vertices pointing outwards.
• Non-convex (or concave) quadrilaterals have one vertex pointing inwards.
Convex
All interior angles less than 180°
Non-convex
One reflex interior angle
■■ Special quadrilaterals
Square Rectangle Rhombus
Parallelogram Kite Trapezium
■■ The angle sum of any quadrilateral is 360.
Polygons can be convex or non-convex.
• Convex polygons have all vertices pointing outwards.
• Non-convex (or concave) polygons have at least one vertex pointing inwards.