Points, lines and angles  (Page 3/3)

The table summarises the special angle pairs that result.

The following video summarises what you have learnt so far

Parallel lines intersected by transversal lines

Two lines intersect if they cross each other at a point. For example, at a traffic intersection two or more streets intersect; the middle of the intersection is the common point between the streets.

Parallel lines are lines that never intersect. For example the tracks of a railway line are parallel. We wouldn't want the tracks to intersect as that would be catastrophic for the train!

All these lines are parallel to each other. Notice the pair of arrow symbols for parallel.

A transversal of two or more lines is a line that intersects these lines. For example in [link] , $AB$ and $CD$ are two parallel lines and $EF$ is a transversal. We say $AB\parallel CD$ . The properties of the angles formed by these intersecting lines are summarised in the table below.

Name of angle	Definition	Examples	Notes
interior angles	the angles that lie inside the parallel lines	in [link] $a$ , $b$ , $c$ and $d$ are interior angles	the word interior means inside
adjacent angles	the angles share a common vertex point and line	in [link] ( $a$ , $h$ ) are adjacent and so are ( $h$ , $g$ ); ( $g$ , $b$ ); ( $b$ , $a$ )
exterior angles	the angles that lie outside the parallel lines	in [link] $e$ , $f$ , $g$ and $h$ are exterior angles	the word exterior means outside
alternate interior angles	the interior angles that lie on opposite sides of the transversal	in [link] ( $a,c$ ) and ( $b$ , $d$ ) are pairs of alternate interior angles, $a=c$ , $b=d$
co-interior angles on the same side	co-interior angles that lie on the same side of the transversal	in [link] ( $a$ , $d$ ) and ( $b$ , $c$ ) are interior angles on the same side. $a+d={180}^{\circ }$ , $b+c={180}^{\circ }$
corresponding angles	the angles on the same side of the transversal and the same side of the parallel lines	in [link] $(a,e)$ , $(b,f)$ , $(c,g)$ and $(d,h)$ are pairs of corresponding angles. $a=e$ , $b=f$ , $c=g$ , $d=h$

The following video summarises what you have learnt so far

Angles

1. Use adjacent, corresponding, co-interior and alternate angles to fill in all the angles labeled with letters in the diagram below:

   

2. Find all the unknown angles in the figure below:

   

3. Find the value of $x$ in the figure below:

   

4. Determine whether there are pairs of parallel lines in the following figures.

   1. 

   2. 

   3. 

5. If AB is parallel to CD and AB is parallel to EF, prove that CD is parallel to EF:

   

The following video shows some problems with their solutions