Year 8 Interactive Maths - Second Edition

## Congruence

If two figures have the same shape and the same size, then they are said to be congruent figures.

For example, rectangle ABCD and rectangle PQRS are congruent rectangles as they have the same shape and the same size.

Side AB and side PQ are in the same relative position in each of the figures.
We say that the side AB and side PQ are corresponding sides.

Congruent figures are exact duplicates of each other.  One could be fitted over the other so that their corresponding parts coincide.

The concept of congruent figures applies to figures of any type.

###### Just to recap the ongoing discussion:
• Angles and sides of two plane figures are said to be corresponding if they are in the same relative positions in each of the figures.
• If one figure coincides with another after a transformation (i.e. a translation, reflection or rotation) that moves the points on the figure but does not alter its angles or side-lengths, then the figures are said to be congruent.

## Congruent Triangles

Congruent triangles have the same size and the same shape.  The corresponding sides and the corresponding angles of congruent triangles are equal.

### Principles of Congruent Triangles

The following principles of congruence are used depending on the information given.

###### 1.  The side-side-side (SSS) principle

Two triangles are congruent if corresponding sides are equal.

###### 2.  The side-angle-side (SAS) principle

Two triangles are congruent if two pairs of corresponding sides and the angle included between the sides are equal.

###### 3.  The angle-side-angle (ASA) principle

Two triangles are congruent if two pairs of corresponding angles and a pair of corresponding sides are equal.

###### 4.  The right angle-hypotenuse-side (RHS) principle

Two right-angled triangles are congruent if the hypotenuses and one pair of corresponding sides are equal.

#### Example 17

Find the values of the pronumerals in the given pair of triangles.  Give reasons for your answers.

#### Example 18

Find the values of the pronumerals in the given pair of triangles. Give reasons for your answers.

#### Example 19

Find the values of the pronumerals in the given pair of triangles.  Give reasons for your answer.

#### Example 20

Find the values of the pronumerals in the given pair of triangles.  Give reasons for your answers.