Key Concepts
- Perform Congruence Transformations
- Identify transformations
Perform Congruence Transformations
What is a transformation?
A transformation is an operation that changes a geometric figure to produce a new figure.
Types of transformations:
Transformations can be divided into 4 types based on the image.
You are viewing: Which Of The Following Is A Congruence Transformation
- Translation
- Rotation
- Reflection
- Dilation
1. Translation:
A translation moves every point of a figure in the same direction and for the same distance.
2. Rotation:
A rotation turns the figure to its fixed point called as the center of rotation.
3. Reflection:
A reflection uses a line of reflection to create a mirror image of the original figure.
4. Dilation:
Dilation is the process of increasing or decreasing the size of the image without changing its shape.
What is a congruence transformation?
A transformation that changes the position of the figure without changing its size or shape is called a congruence transformation.
Translations, reflections, and rotations are the three types of congruence transformations.
Identify transformations
Example 1:
Identify the type of transformation in the following images.
Solution:
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a. Reflection in a horizontal line.
b.Rotation about a point.
c.Translation in a straight path.
Example 2:
The vertices of a quadrilateral ABCD are A (- 4, 3), B (- 2, 4), C (- 1, 1), and D (- 3, 1). Draw a figure and its image after the translation (x,y)→(x+5,y−2).x,y→x+5,y−2.
Solution:
Draw a quadrilateral ABCD. Find the translation of each vertex by adding 5 to its x – coordinate and subtract 2 from its y – coordinate.
Example 3:
In the given figure, use a reflection in X-axis to draw the other half of the pattern.
Solution:
To find the corresponding vertex in the image, multiply the Y-coordinate of the vertex by – 1.
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Example 4:
Graph AB and CD with the given vertices, A (- 3, 1), B (- 1, 3), C (1, 3), D (3, 1). Give the angle and direction of rotation.
Solution:
We first draw AB and CD with the given vertices.
From the above figure,
m∠AOC=m∠BOD=90°
∴The given vertices form an angle of 90°clockwise rotation.
Example 5:
The vertices of a triangle ABC are A (4, 4), B (6, 6), C (7, 4), and the notation (x,y)→(x+1, y−3)(x,y)→(x+1, y−3) indicates the translation of ∆ABC to ∆DEF. Prove that ∆ABC≅∆DEF to verify the translation, a congruence transformation.
Solution:
From the above figure and the given vertices,
Exercise
- Identify the transformation in the given figure.
- In the given image ABCD with the coordinates Draw its image after the translation.
- Describe the translation with the given coordinates: 2 units to the right, 1 unit down.
- Draw the other half of the given figure using -axis reflection.
- Graph AB and CD using the coordinates A (1, 2), B (3, 0), C (2, -1), D (2, –3) and give the angle of rotation.
- Find the corresponding point in the figure with the given point and translation of an image.Point on image: (4, 0); translation:
- Describe the translation with the given coordinates: 6 units to the right, 3 units down.
- Identify the transformation in the given figure
- Draw the other half of the given figure using -axis reflection.
- Identify the type of transformation in the given image.
Concept Map
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Category: WHICH