Mathematics Form 1-4 : CHAPTER TWENTY EIGHT – REFLECTION AND CONGRUENCE

Specific Objectives

By the end of the topic the learner should be able to:

1. State the properties of reflection as a transformation
2. Use the properties of reflection in construction and identification of images and objects
3. Make geometrical deductions using reflection
4. Apply reflection in the Cartesian plane
5. Distinguish between direct and opposite congruence
6. Identify congruent triangles.

Content

1. Lines and planes of symmetry
2. Mirror lines and construction of objects and images
3. Reflection as a transformation
4. Reflection in the Cartesian plane
5. Direct and opposite congruency
6. Congruency tests (SSS, SAS, AAS, ASA and RHS)

Introduction

The process of changing the position, direction or size of a figure to form a new figure is called transformation.

Reflection and congruence

Symmetry

Symmetry is when one shape becomes exactly like another if you turn, slide or cut them into two identical parts. The lines which divides a figure into two identical parts are called lines of symmetry. If a figure is cut into two identical parts the cut part is called the plane of symmetry.

How many planes of symmetry does the above figures have?

There are two types of symmetry. Reflection and Rotational.

Reflection

A transformation of a figure in which each point is replaced by a point symmetric with respect to a line or plane e.g. mirror line.

Properties preserved under reflection

• Midpoints always remain the same.
• Angle measures remain the same i.e. the line joining appoint and its image is perpendicular to the mirror line.
• A point on the object and a corresponding point on the image are equidistant from the mirror line.

A mirror line is a line of symmetry between an object and its image.

Examples

To reflect an object you draw the same points of the object but on opposite side of the mirror. They must be equidistance from each other.

Exercise

Find the mirror line or the line of symmetry.

To find the mirror line, join the points on the object and image together then bisect the lines perpendicularly. The perpendicular bisector gives us the mirror line.

Congruence

Figures with the same size and same shape are said to be congruent. If a figure fits into another directly it is said to be directly congruent.

If a figure only fits into another after it has been turned then it’s called opposite congruent or indirect congruence.

C

 A B

Figure A and B are directly congruent while C is oppositely or indirectly congruent because it only fits into A after it has been turned.

End of topic