**3.1- Introduction**

• Calculate unknown angles and give simple explanations using the

following geometrical properties:

(a) angles at a point

(b) angles at a point on a straight line and intersecting straight lines

(c) angles formed within parallel lines

(d) angle properties of triangles and quadrilaterals

(e) angle properties of regular and irregular polygons

(f) angle in a semi-circle

(g) angle between tangent and radius of a circle

(h) angle at the centre of a circle is twice the angle at the circumference

(i) angles in the same segment are equal

(j) angles in opposite segments are supplementary

Angle properties of polygons includes angle sum.

** 3.2- Angles and lines**

Lines AB and CD are parallel to one another (hence the » on the lines).

a and d are known as **vertically opposite angles**. Vertically opposite angles are equal. (b and c, e and h, f and g are also vertically opposite).

g and c are **corresponding angles**. Corresponding angles are equal. (h and d, f and b, e and a are also corresponding).

d and e are **alternate angles**. Alternate angles are equal. (c and f are also alternate). Alternate angles form a ‘Z’ shape and are sometimes called ‘Z angles’.

a and b are adjacent angles. Adjacent angles add up to 180 degrees. (d and c, c and a, d and b, f and e, e and g, h and g, h and f are also adjacent).

d and f are **interior angles**. These add up to 180 degrees (e and c are also interior).

Any two angles that add up to 180 degrees are known as **supplementary angles**.

**3.3- Triangles and Quadrilaterals**

Using some of the above results, we can prove that the sum of the three angles inside any triangle always add up to 180 degrees.

A quadrilateral is a shape with 4 sides.

For any quadrilateral, we can draw a diagonal line to divide it into two triangles. Each triangle has an angle sum of 180 degrees. Therefore the total angle sum of the quadrilateral is 360 degrees.

3.4- Congruence and Similarity

• Solve problems and give simple explanations involving similarity and

congruence

• Calculate lengths of similar figures

• Use the relationships between areas of similar triangles, with

corresponding results for similar figures, and extension to volumes

and surface areas of similar solids

3.5- Polygon angles

The exterior angles of a shape are the angles you get if you extend the sides.

A polygon is a shape with straight sides. All of the exterior angles of a polygon add up to 360° because if you put them all together they form the angle all the way round a point

**3.6- Summary and Review**

**3.7- Assessment 3**

**Question 1-** Calculate the sum of interior angles of an octogon and a decagon?

**Question 2-** Which of these shapes has the most sides? Hexagon, Octagon, Triangle, Rhombus.

**Question 3 –** AB, CD and EF are straight lines. We assumes that AB and CD are parallel. What is the angle y?

**Question 4 :** AB is not parallel to CD. Angle w is 60° , What is angle y?