Year 8 Angles and geometrical figures: revision mind map

1Reviewing angles

Complementary angles add to 90°. Supplementary angles add to 180°. Vertically opposite angles are equal.

35° has a complement of 55° and a supplement of 145°

Angles on a straight line add to 180°

Angles around a point add to 360°

Acute: under 90°. Right: 90°. Obtuse: 90° to 180°. Reflex: over 180°.

2Transversal and parallel lines

With parallel lines: corresponding angles are equal (F), alternate angles are equal (Z), co-interior angles add to 180° (C).

If one angle is 70°: corresponding 70°, alternate 70°, co-interior 110°

Watch out: these rules only work when the lines are parallel.

3Triangles

Angles add to 180°. An exterior angle equals the two opposite interior angles added together.

Angles 40° and 75°: the third is 65°, the exterior angle is 115°

Equilateral: all angles 60°

Isosceles: two equal sides, two equal base angles

4Quadrilaterals

Angles add to 360°.

Angles 80°, 95°, 110°: the fourth is 75°

Parallelogram: opposite angles equal

Rhombus: all sides equal

Kite: one pair of opposite angles equal

5Polygons

Angle sum of an $n$-sided polygon: $S = (n - 2) \times 180^\circ$.

Pentagon: $3 \times 180^\circ = 540^\circ$, each angle of a regular one is $108^\circ$

Hexagon: $4 \times 180^\circ = 720^\circ$, each angle of a regular one is $120^\circ$

63D solids and Euler's formula

For solids with flat faces: $F + V = E + 2$ (faces, vertices, edges).

Cube: $6 + 8 = 12 + 2$ ✓

Triangular prism: $5 + 6 = 9 + 2$ ✓

Prisms have two matching ends. Pyramids come to a point.

73D coordinates

A point is $(x, y, z)$: along, across, then up. The origin is $(0, 0, 0)$.

$(2, 3, 4)$ is 2 along the x-axis, 3 along the y-axis and 4 up the z-axis

A 5 by 3 by 2 box with a corner at the origin has its opposite corner at $(5, 3, 2)$