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