# GM5-5: Deduce the angle properties of intersecting and parallel lines and the angle properties of polygons and apply these properties.

Elaboration on this Achievement Objective

This means that students will know and apply angle properties relating to intersecting and parallel lines.

The angle properties of lines are:

- Vertically opposite angles are equal, for example a = d, b = c
- Adjacent angles add to 180
^{o, }for example a + b = 180^{o}, a + c = 180^{o} - Corresponding angles are equal, for example a = e, b = f, c = g, d= h
- Interior angles add to 180
^{o}, for example c + e = 180^{o}, d + f = 180^{o} - Alternate angles are equal, c = f, d = e

Students should apply the properties of intersecting and parallel lines to problems like constructing rectangular and skewed picture frames.

Students should find and apply the angle properties of polygons. They may find the formula for the internal angles of regular polygons (equal angles) by measuring and creating a table of results or by reasoning through cutting the polygons into triangles. These angles properties are:

- Interior angles of a polygon with n sides are ((n-2) x 180
^{o})/n. - Exterior angles of any polygon add to 360
^{o}.