Angles and Lines

Slideshow 36, Mathematics

Mr Richard Sasaki, Room 307

Objectives

Review angle properties learned so farUnderstand alternate anglesCalculate missing angles at certain points

Angle PropertiesLet’s have a look back at what we have learned so far.

A polygon with n sides has a sum of interior angles ___________.

Any polygon has sum of exterior angles ________.

180(n-2)o

360o

At a point, a polygon’s interior and exterior angle add up to ________.180o

Angle Properties

A right-angle is exactly _______.90o

On an Equilateral triangle, each angle is ______.60o

On two straight lines, opposite angles are always ________.equal

Angle Properties

𝑥180𝑜−𝑥

A pair of parallel lines have two corresponding angles between them that add up to _______.180o

𝑥360𝑜−𝑥

All angles around a point add up to _______.360o

Try the first worksheet!

Answers1. 1

2. b.

3. c.

4. d.

5. e.

6. f.

7. 2. 72o

8. 3.

1. 1

2. b.

3. c.

4. d.

5. e.

6. f.

7. 2.

Alternate AnglesYou should have found out from the last question on the worksheet that o and e are the same size.

e

o

These are called alternate angles and are shaped in like a “Z” format where the top and bottom lines are parallel.

Naming Lines and Angles

Lines are often labelled and this gives the ability to name angles.

A B

C D

E

F

Here we can see lines AB, CD and EF. (Note: Line AB and BA are the same.)

Lines are of infinite length. Lines that aren’t are called line segments.

𝑥Angle can be known as AEF or FEA.

Line SegmentsShapes are usually made of line segments.

A B

C D

Here, AB, AC, CD and BD are line segments.

Which two line segments are parallel?

AB and CD

We can denote this as AB CD.

(“” means parallel.)

Let’s try the Activote exercise.

Acute, Obtuse or Reflex?We know that a right-angle is 90o, there is 180o on a line and 360o around a point but how about in between?

Between 00 and 90o Acute

Between 900 and 180o

Obtuse

Between 1800 and 360o Reflex

Try the final worksheet!

Answers 1. Acute, obtuse, right-angleAcute, straight, reflexReflex, acute, right-angle2. Reflex3. It must be acute, a right angle or obtuse4. 45. AB CD, (or

6. Line, line segment