S2N2 : Congruence and Similarity

Congruence and Similarity

Congruence

Two figures are congruent if they have the same shape and size,

=> All corresponding angles are equal

      All corresponding sides are equal

Pairs of Congruent shapes

Pairs of shapes are Not Congruent

Congruence and Transformation

In geometry, reflection, translation and rotation are called transformation. 

During a transformation, the object is 'transformed' to its image.

Reflection

1. Point A and Point B are equidistant from  line MN
2. Point B and R are equidistant from line MN
3. Point C and Q are equidistant from line MN
4. The sides and angles of ABC and PQR are the same

=> ABC is congruent to its image under a reflection.

Translation <Shifting>:

ABC is shifted by a vector PQ to PQR

Point A, B and C are shifted by a vector XY to Point PQR

ABC is congruent to its image under a translation.

Rotation 

ABC has a rotation of 90 with centre at O to PQR

=> ABC is congruent to its image PQR under a rotation

Tessellation

=> covering a plane/surface by congruent figures of one type of a few types without any gaps or overlap. 

Example

Similarity

The original objects and its image are of the same shapes but of different size through:  

Enlargement - increase in size

Reduction - reduce in size

An enlargement / reduction is a type of transformation with a scale factor.

Scale factor

 = Length of side of the image / length of the corresponding side of the object

Scale Drawing

Reduced / enlarged drawings of actual objects

The scale of a drawing can be expressed as :- 

                         ratio 1 : n 

 

      where 1 unit on the drawing represents n units on the actual object.

      1 : 120 => 1 cm on the drawing represents 120 cm on the actual object.