Angles, Polygons and Bearings: notes

Angle Facts

• Angles on a straight line add to 180 degrees. Angles at a point add to 360 degrees.
• Triangle: angles add to 180 degrees. Quadrilateral: angles add to 360 degrees.
• Parallel lines: alternate angles are equal (Z shape), corresponding angles are equal (F shape), co-interior angles add to 180 degrees (C shape).
• Isosceles triangle: two equal sides and two equal base angles.

Polygons

• Sum of interior angles: (n - 2) x 180 degrees. A hexagon has 4 x 180 = 720 degrees.
• Exterior angles of any polygon add to 360 degrees. A regular polygon has exterior angle 360 / n.
• Interior angle + exterior angle at a vertex = 180 degrees.

Similar and Congruent Shapes

• Congruent: same shape and same size.
• Similar: same shape, different size. Matching sides are in the same ratio, the scale factor.

Bearings and Loci

• Three-figure bearing: measured clockwise from north, always written with three figures. East is 090, south is 180.
• Back bearing: add or subtract 180 degrees.
• Locus: the path of a point following a rule. Points a fixed distance from a point make a circle; points equal distance from two points make the perpendicular bisector.