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MATHEMATICS: FORM ONE: Topic 6 - GEOMETRY

TOPIC 6: GEOMETRY

The Concept of a Point

Explain the concept of a point

Aindicate – is a smallest geometric effigy 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 depict a line

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

A line passing through two points e.one thousand A and B and extends without terminate(i.eastward infinitely) in both directions is denoted by

The Deviation Betwixt a Line, a Line Segment and a Ray

Distinguish betwixt 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.Information technology is denoted past

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

Measuring Angles of Dissimilar Size Using a Protractor

Measure out angles of different size using a protractor

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

Example 1

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

Solution

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

Consider a line segment crossing 2 parallel line segments. This line is chosen atransversal

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

They are too chosen Z -angles

<!--[endif]-->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

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

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

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

Construct an bending of 60° using a pair of compasses

Angle of 60°

Bisection of a Given Angle

Bifurcate a given bending

Copying a Given Bending by Construction

Copy a given angle past construction

Action 2

Copy a given bending by construction

Parallel Lines

Construct parallel lines

Parallel lines tin can be shown as below:

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.

A Polygon and a Region

Describe a polygon and a region

Apolygonis a plane effigy whose sides are iii or more co planar segments that intersect only at their endpoints. Consecutive sides cannot exist collinear and no more two sides can encounter at any one vertex.

Apolygonal regionis defined equally a polygon and its interior.

Dissimilar Types of Triangles

Construct different types of triangles

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

Aright – angled triangle – has one angle equal to 90º

Anisosceles triangle – has two equal sides and two equal angles

Anequilateral triangle – has three equal sides and all angles equal

Note:A triangle with all sides different and all angles dissimilar is chosen scalene triangle.

A triangle with verticesA, B andCis denoted every bit

A triangle has two kinds of angles

  1. Interior angles
  2. Exterior angles

Interior angle – is an angle within the triangle.The sum of interior angles of a triangle is 180.

Case, consider the triangle below

Exterior angle - is an angle exterior the triangle. Consider the triangle below

Case two

Observe the angles x and y in the diagrams below

Unlike Quadrilaterals

Construct unlike 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

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

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

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

A kite – has ii pairs of next sides equal.One pair of opposite angles are also equal

A trapezium – has one pair of reverse sides pair

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

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

Example iii

Find the anglesten andy in the diagrams below

Solution

To brand a circle: Depict a curve that is "radius" abroad from a central betoken.

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

You can describe it yourself: Put a pivot in a board, put a loop of string effectually information technology, and insert a pencil into the loop. Continue the string stretched and draw the circle!

Different Parts of a Circle

Depict dissimilar parts of a circle

Theradiusof the circle is a straight line drawn from the eye to the boundary line or the circumference. The plural of the discussion radius isradii.

Thediameteris the line crossing the circle and passing through the middle. Information technology is the twice of the length of the radius.

Thecircumferenceof a circle is the boundary line or the perimeter of the circumvolve.

Anarcis a function of the circumference between two points or a continuous piece of a circle. The shorter arc between P and Q is chosen theminor arc. The longer arc betwixt Q and P is chosen themajor arc.

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

Asemi-circleis an arc which is half of the circumference.

Atangentis a straight line which touches the circle. It does not cut the circumference. The signal at which it touches, is called thebespeak of contact.