Geometry

Hong Kong

Stage 1 - Stage 3

Lesson

Let me show you different kinds of lines and how we label them.

(slide the slider to change line types and move the points around)

**Line**: passes through two points and extends to infinity in both directions, notated

**Line segment (interval)**: starts at a point and ends at a point, notated

**Ray**: starts at a point and extends through a second point to infinity, notated

Now, let me show you different types of angles. Play with this applet to explore the different types of angles, what they look like and how big they are. Slide the slider and watch the angle change.

Complementary angles are angles that sum to $90$90°. In the diagram on the right, $\angle DOC$∠`D``O``C` and $\angle COB$∠`C``O``B` are complementary.

Supplementary angles are angles that sum to $180$180°. In the diagram on the right, $\angle COD$∠`C``O``D` and $\angle DOE$∠`D``O``E` are supplementary angles.

**Acute**: an angle *between *0° and 90°

**Right: **an angle of *exactly *90°

**Obtuse**: an angle of *between *90° and 180°

**Straight**: an angle of *exactly *180°

**Reflex**: an angle of *between *180° and 360°

**Revolution**: an angle of *exactly *360°

**Complementary**: angles that *sum to* 90°

**Supplementary**: angles that *sum to *180°

This quadrilateral has 4 vertices. They are labelled $A$`A`, $B$`B`, $C$`C` and $D$`D`.

The edges of the shape would be labelled like line segments.

We can call them **AB**, **BC**, **CD**, **DA **.

The angle marked has **vertex **(the pointy bit of the angle) at $B$`B`.

We label an angle by moving from one point on the line segment, through the VERTEX to a point on the the other line segment. Thus the shaded angle is called $\angle ABC$∠`A``B``C` or $\angle CBA$∠`C``B``A`. See the angle symbol at the front? This is important; it tells us that the three point names that follow make up the angle which we are talking about.

Can you see where $\angle ADC$∠`A``D``C` is ? What about $\angle DCB$∠`D``C``B` ?

Lines, Line Segments (intervals) and Rays that cross create angles.

Have a play with this applet, you can create lines, line segments and rays that cross each other. Change the slider to change the type of lines, move the points to place you like, then slide the slider to show the angles that are created.

Labelling angles

We label an angle by moving from one point on the line (line, segment or ray), through the VERTEX to a point on the the other line (line, segment or ray).

In the following, state the vertex and name the angle.

Is this angle ACUTE, OBTUSE or REFLEX?

In the diagram, $\angle ABD=53^\circ$∠`A``B``D`=53°, $\angle ABE=112^\circ$∠`A``B``E`=112° and $\angle DBC=131^\circ$∠`D``B``C`=131°

a) Find the measure of $\angle EBD$∠`E``B``D`

b) Deduce the measure of $\angle EBC$∠`E``B``C`