Year 9 Interactive Maths - Second Edition

Congruence

Square ABCD is congruent to square EFGH as their corresponding sides and angles are equal.

Note:

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

The concept of congruence applies to figures of any type.  In this section we will consider congruent triangles, principles of congruent triangles and their applications.

Congruent Triangles

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

Note:

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 20

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

Solution:

Example 21

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

Solution:

Example 22

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

Solution:

Example 23

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

Solution:

Example 24

Solution:

As required.

Example 25

Solution:

As required.

Key Terms

congruent figures, congruent triangles, corresponding sides, corresponding angles, principles of congruent triangles, side-side-side (SSS) principle, side-angle-side (SAS) principle, angle-side-angle (ASA) principle, right angle-hypotenuse-side (RHS) principle