| 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.
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 17
Find the values of the pronumerals in the given pair of triangles. Give
reasons for your answers.
Solution:
Example 18
Find the values of the pronumerals in the given pair of triangles. Give
reasons for your
answers.
Solution:
Example 19
Find the values of the pronumerals in the given pair of triangles. Give
reasons for your answer.
Solution:
Example 20
Find the values of the pronumerals in the given pair of triangles. Give
reasons for your answers.
Solution:
Key Terms
congruence, congruent figures, corresponding
angles, corresponding sides, congruent
triangles |
