chapter 2 angles and shapes updated 2013

Form 1 [CHAPTER 2: ANGLES AND SHAPES]

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Chapter 2: Angles and Shapes 2.1 Introduction Key Concepts: What is an angle? Types of angles (acute, obtuse, reflex, right angle) Measuring and drawing angles (Using a protractor)

What is an angle?

An angle is a measure of turn.

There are many types of angles.

Right Angle

A right angle is exactly 90. The lines making a right angle

are called perpendicular. Lines AB and BC are

perpendicular. This angle can be written as angle ABC the

letter in the centre is the actual point the other two are the

points from which the angle is binded. In this case: angle

ABC = 90.

Acute angle

Angles which are smaller than a right angle are called acute angles.

Obtuse angles

Angles larger than a right angle but smaller than a straight line are

called obtuse.

B

A

C



Reflex angles

Angles which are larger than a straight line are called

reflex angles.

Task 1:

Look at this letter A. How many acute angles can you see? ____________________. How many obtuse angles? ___________________. What about reflex angles? _____________________.

Measuring and drawing angles:

Degrees () are the units used for angles. To measure the angles we need an apparatus

called protractor.

How to use the protractor

The protractor has two sets of numbers. This is because angles are not always drawn

clockwise sometimes they are drawn anticlockwise.

ClockwiseAnti clockwise



Measuring an angle

1. The centre of the protractor must be place exactly on the vertex of the angle

being measured.

2. One of the lines coming out of the vertex has to be placed exactly on the

horizontal line on the protractor.

3. Read till were the angle rises on the protractor. Always start measuring from

zero degrees.

You can now practice measuring angles using a protractor: WS pg 10 number 2; F1 pg

29 number 3, 4.

Drawing Angles:

Example :Draw an angle of 57

Step 1:

Draw a line across a clean sheet of paper, about

half way down the page. Put a line near one of the

ends of the line. This is where the angle will be.

Step 2

Put the centre of the protractor on the

mark with the start line of the protractor

over the line you have drawn.



Step 3

Do a mark on the paper next to the 57

Step 4

Take away the protractor and use your ruler to draw a straight line through the two

marks.

Step 5

Draw the arc and label the angle.

57



In the following space draw an angle of 79.

Support exercises: F1 pg 29 nos. 1 4, pg 31 nos. 1, 2, 3; WS pg 10 nos. 1, 2, 3. 2.2 Finding angles Key Concepts: Angles at a point Angles on a straight line Vertically opposite angles

Angles at a point A + B + C + D = 360 Angles at a point add up to 360.

Example 1: Find the missing angle (Give a reason for your answer).



Angles on a straight line A + B = 180 Angles on a straight line add up to 180.


Vertically opposite angles

Vertically opposite angles are equal.


Support exercises: F1p. 33 no. 1; WS p. 10 nos 4 a,b,c,f; p.11 nos. 1,2.



2.3 Triangles Key Concepts: Isosceles triangle Equilateral triangle

What are triangles? How do you recognize a triangle?

Triangles have 3 sides and 3 angles. Isosceles triangle

Measure all sides and angles using a ruler and protractor.

Isosceles triangles have ____________ equal sides and

____________ equal angles.

Equilateral triangle

Measure all sides and angles using a ruler and protractor. Equilateral triangles have ____________ equal sides and

____________ equal angles which are equal to

_____________.

Support exercises: F1 pg 107 no.1.



2.4 Quadrilaterals What are quadrilaterals? How do you recognize a quadrilateral?

Quadrilaterals have 4 sides and 4 angles. Square

Measure all sides and angles using a ruler and protractor. A square has __________ sides equal. A square has __________ angles equal which are

equal to __________.

Rectangle Measure all sides and angles using a ruler and protractor.

A rectangle has opposite sides _________. A rectangle has __________ angles equal

which are equal to __________.

Parallelogram

A Parallelogram has opposite angles

______________. Opposites sides are

_______________ and ______________.



Trapezium

A Trapezium has an _____________ pair

of parallel sides. It has

________________ equal sides

Rhombus

A Rhombus has _______________ sides equal.

Opposites sides are _______________ and

opposite angles are ______________.

Support exercises: F1 p. 107 nos. 2, 4; WS p. 12 no. 1. 2.5 Finding angles Key Concepts: Angles in a triangle Angles in a quadrilateral

Angles in a triangle Activity: Cut the corners of the given triangle and put them together below They make a _________ _________. The angles in a triangle add up to _______



Angles in a Quadrilateral Activity: Cut the corners of the given quadrilaterals and put them together below They make a _________ . The angles in a quadrilateral add up to _______ . Example 1: Find the missing angle.

Example 2:Find the missing angle.

Support exercises: F1p. 35 no. 1; WS p.13 nos. 1,2,3,6, p.10 no 4 g, h, l; p.11 no. 3.



2.6Angles and Lines Key Concepts: Parallel lines Perpendicular lines Intersecting lines

Parallel lines

The two lines point in the same direction. They do not meet or cross,

and if you made them longer they still would not meet or cross. These

are parallel lines. The distance between two parallel lines remains the

same.

The following two lines do not point in the same direction

If we lengthen them they will meet.

These lines are called intersecting lines since they intersect at a point.

Perpendicular lines.

Perpendicular lines intersect at 90.

Lines AB and BC are said to be perpendicular to each other.



2.7 Alternate angles Key Concept: Alternate angles

Example 1: Find the missing angles giving reasons for your answers.

Support exercises: F1p. 33 no. 2; WS p. 10 nos. 4 d, e; p. 12 no. 2.

Alternate angles are equal

A



2.8 Corresponding angles Key Concepts: Corresponding angles.

Example 2: Find the missing angles giving reasons for your answers.

Support exercises: F1p. 33 no. 2; WS p. 10 nos. 4 d, e; p. 12 no. 2.



2.9Mixed Examples Key Concepts: Working mixed examples.

Example: Find the angles marked with a letter giving reasons.



Support exercises: F1p. 33 no. 3; p. 35 no. 2 WS p.13 nos. 4, 5, 6, 7, 8; p.10 no. 6;

chapter 2 angles and shapes updated 2013

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