# 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)...

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