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Subsection 2.3.4 Rotation and Congruence
Activity 2.3.6 .
Copy the trangle
\(ABC\) and the point
\(D\) on a graph paper. Using a ruler and a protractor, rotate the triangle
\(-90^\circ\) about point
\(D.\)
Draw a dotted line to connect vertex
\(A\) to point
\(D\)
Place a protractor at the line
\(AD\) with the centre of the protractor at
\(D\) and measure
\(90^\circ.\) Using a ruler draw
\(DA'\) such that
\(AD\,=\,DA'.\)
Repeat the step above for for vertices
\(B \text{ and} C.\)
Congruence refers to a relationship between two figures or objects, whereby, they are identical in size and shape.
Rotation is a type of transformation that repositions an object but preserves the shape and size of the object. Thus, rotation produces congruent figures.
\(\Delta ABC \) and
\(\Delta A'B'C' \) are similar in size and shape. Therefore, they are said to be directly congruent.
Example 2.3.17 .
Triangle
\(ABC\) is mapped onto
\(A'B'C'\) after a rotation of
\(-45^\circ\) and centre of rotation
\(D.\)
\(\Delta ABC \text{ and } \Delta A'B'C'\) have the same shape and size.
The length of the corresponding sides of
\(\Delta ABC \text{ and } \Delta A'B'C'\) are the same.
Every corresponding internal angle for the triangles remain the same.
Therefore,
\(\Delta ABC \text{ and } \Delta A'B'C'\) are said to be
directly congruent.
Exercises Exercises
1. Identify the axes of rotational symmetry and their respective order in the following:
2. Identify the axes of rotational symmetry and their respective order for the following figures:
