Join
Topic

Geometry

Estimated reading: 6 minutes 513 views Contributors

Points and Lines

The Concept of a Point

Explain the concept of a point

A point – is a smallest geometric figure which gives a position of object in a plane

A line segment – is a straight line joining two points in a plane

The Concept of a Point to Draw a Line

Extend the concept of a point to draw a line

A line segment – is a straight line joining two points in a plane

line 1455622622614

A line passing through two points e.g A and B and extends without end (i.e infinitely) in both directions is denoted by

line 1455623009316

The Difference Between a Line, a Line Segment and a Ray

Distinguish between a line, a line segment and a ray

A ray – is a line starting from a point, say A and pass through a point, say B and extends without end in one direction.It is denoted by

line 1455623243959

Angles and Lines

Angles

Draw angles

An angle – is a measure of an amount of turn. For instance, a complete turn has an angle of 360º

angle 1455623551435

Measuring Angles of Different Size Using a Protractor

Measure angles of different size using a protractor

There are several types of angles including:- acute, right, complementary, obtuse, supplementary and reflex angle

angle 1455624515959
angle 1455625103819
angle 1455625260707

Example 1

  1. Two angles are supplementary. One angle is three times the other. What are the angles?
  2. Two angles are complementary. One angle is 40º greater than the other. What are the angles?

Solution

Solution 1455625578489

Drawing Angles Using a Protractor

Draw angles using a protractor

The angles formed by crossing lines includes vertically opposite angles, alternate angle and corresponding angles

Vertically opposite angles

The angles on the opposite sides of the crossing lines are equal

line 1455627062599

Alternate angles

Consider a line segment crossing two parallel line segments. This line is called a transversal

line 1455627211388

The angles within the parallel line segments on the opposite sides of the transversal are equal

line 1455627354160

They are also called Z – angles

Corresponding angles

The angles on the same side of the transversal and on the same side of the parallel lines are equal.They are called corresponding angles and sometimes called F – angles

line 1455627602909

There are also three other pairs of corresponding angles in the diagram above.When showing that two angles are equal you must give reason whether they are vertically opposite, or alternate or corresponding angles.

Constructions

Construction of a Perpendicular Bisector to a Line Segment

Construct a perpendicular bisector to a line segment

Perpendicular Bisector to a Line Segment is shown below

bisector 1455628269499

Contruction of an Angle of 60° Using a Pair of Compasses

Construct an angle of 60° using a pair of compasses

Angle of 60°

angle 1455628461149

Bisection of a Given Angle

Bisect a given angle

Activity 1

Bisect a given angle

Copying a Given Angle by Construction

Copy a given angle by construction

Activity 2

Copy a given angle by construction

Parallel Lines

Construct parallel lines

Parallel lines can be shown as below:

parallel lines 1455642684884

Different Types of Angles Formed by Parallel Lines and a Transversal

Identify different types of angles formed by parallel lines and a transversal

Different types of angles are shown below.

lines 1455642888121

Polygons And Regions

A Polygon and a Region

Describe a polygon and a region

Apolygonis a plane figure whose sides are three or more coplanar segments that intersect only at their endpoints. Consecutive sides cannot be collinear and no more than two sides can meet at any one vertex.

Apolygonal regionis defined as a polygon and its interior.

Different Types of Triangles

Construct different types of triangles

A triangle – is a polygon with three sides.The sides connect the points called vertices

A right – angled triangle – has one angle equal to 90º

right 1455644712296

An isosceles triangle – has two equal sides and two equal angles

angle 1455644824992

An equilateral triangle – has three equal sides and all angles equal

angle 1455644996304

NOTE:A triangle with all sides different and all angles different is called scalene triangle

angle 1455645139441

A triangle with vertices A, B and C is denoted as

angle 1455645512462

A triangle has two kinds of angles

  1. Interior angles
  2. Exterior angles

Interior angle – is an angle inside the triangle.The sum of interior angles of a triangle is

Example, consider the triangle below

angle 1455646497867

Exterior angle – is an angle outside the triangle.Consider the triangle below

angle 1455646684262

Example 2

Find the angles x and y in the diagrams below

example 1455647064901

Different Quadrilaterals

Construct different quadrilaterals

A quadrilateral – is a polygon with four sides.Examples of quadrilaterals are a square, a rectangle, a rhombus, a parallelogram, a kite and a trapezium

A square – has equal sides and all angles are 90º

angle 1455647312408

A rectangle – has two pairs of opposite sides equal and all angles are 90º

angle 1455647426457

A rhombus – has all sides equal.Opposite angles are also equal

angle 1455647551823

A parallelogram – has two pairs of opposite sides equal.Opposite angles are also equal

angle 1455647717592

A kite – has two pairs of adjacent sides equal.One pair of opposite angles are also equal

angle 1455647906093

A trapezium – has one pair of opposite sides pair

angle 1455648060663

Any quadrilateral is made up of two triangles. Consider the below quadrilateral.

angle 1455648270481

Sum of angles of quadrilateral = 2 ×180º = 360º

Example 3

Find the angles x and y in the diagrams below

angle 1455650053841

Solution

angle 1455650213174

Circles

A Circle

Draw a circle

To make a circle: Draw a curve that is “radius” away from a central point.

circle 1455650697504

And so:All points are the same distance from the center.

You can draw it yourself:Put a pin in a board, put a loop of string around it, and insert a pencil into the loop. Keep the string stretched and draw the circle!

Different Parts of a Circle

Describe different parts of a circle

The radius of the circle is a straight line drawn from the center to the boundary line or the circumference. The plural of the word radius is radii.

circle 01 1455651221051

The diameter is the line crossing the circle and passing through the center. It is the twice of the length of the radius.

circle 02 1455651371747

The circumference of a circle is the boundary line or the perimeter of the circle.

circle 03 1455651464617

An arc is a part of the circumference between two points or a continuous piece of a circle. The shorter arc between and is called the minor arc. The longer arc between and is called the major arc.

circle 03 1455651717230

The chord is a straight line joining two points on the circumference points of a circle. The diameter is a special kind of the chord passing through the center.

circle 03 1455651584482

Asemi-circleis an arc which is half of thecircumference.

circle 03 1455651887227

A tangent is a straight line which touches the circle. It does not cut the circumference. The point at which it touches, is called the point of contact.

circle 07 1455652115877
Geometry - PreviousApproximationsNext - GeometryAlgebra

Related articles

Leave a Comment


Share this Doc

Geometry

Or copy link

CONTENTS

Made with ❤️ by Darasa Huru

Learning BaseContact

Thrive! English Standard Four PDF-Free Download

Do you want to see your primary school student express themselves with absolute

Excel Now! Hisabati Darasa La Tatu PDF [Download Bure]

Je, unatafuta njia rahisi ya kumsaidia mwanafunzi wako kufanya vizuri na kupenda

Thrive! Civic and Moral Standard Three PDF [Free Download]

Looking for the official TIE Civic and Moral Standard Three textbook? Access thi

Thrive! English Standard Three PDF-Free Download

Looking for the official TIE English Standard Three textbook? Grab this free dig

Learn with Joy: Social Studies Standard Three PDF Free

Need the official TIE Social Studies Standard Three textbook? Get the free digit

Ignite Curiosity! Download the Official Standard 3 Science Technology Book Free

Looking for the official TIE Science and Technology Standard Three textbook? Gra

Master Mathematics Standard Three Textbook PDF [Free Download]

Need the Mathematics Standard Three textbook? This free PDF follows the Tanzania

English Standard Five

Are you looking for the English Standard Five textbook for primary schools in Ta

Standard Seven

Excel! Social Studies Standard Four PDF [Free Download]

Need the Social Studies Standard Four textbook? This free PDF follows the Tanzan

Thrive! Civic and Moral Education Standard Four PDF Free

Download Civic and Moral Education Standard Four book PDF. Covers TIE syllabus t

Standard Six

Chat Icon Close Icon

Subscribe

×
Cancel