Similar Figures
Next
Define Similar Figures:
- Understand the definition of similar figures and how they differ from congruent figures.
- Identify the symbol used to denote similarity (~).
Recognize Properties of Similar Figures:
- Describe the properties of similar figures, emphasizing that they have the same shape but different sizes.
- Understand that corresponding angles in similar figures are equal, and corresponding sides are proportional.
Understand Transformations Leading to Similarity:
- Differentiate between rigid transformations (translation, rotation, reflection) that yield congruent figures and non-rigid transformations (dilation) that yield similar figures.
- Explain how dilations affect the size of a figure while preserving its shape.
these text boxes
In this lesson click to show more information.
Review
Back
Next
Congruent figures are ____ that are exactly the same shape and size. The symbol to show congruence is ≅.
figures
Rigid Transformations are transformations that change orientation but do not change shape or size. Rigid transformations will always yield congruent figures.
Translation
Reflection
Rotation
Similar Figures
Back
Next
rigid transformations
We know that when one or more ____________________ occur, the ________ and the image are congruent. But, we have one more transformation, dilation, which is not rigid.
preimage
When a dilation occurs, the preimage and image are similar. Similar figures are figures that have the same shape but different sizes. The symbol to show similarity is ~.
Similar Figures
Back
Next
Below is an example of a similar figure:
Scale Factor
What do notice about the side lengths? What do you notice about the angles?
Info
Info
Practice
Back
Next
Please complete to check your understanding.
Try it
Are the following similar figures?
Practice
Back
Next
Please complete to check your understanding.
Try it
Are the following similar figures?
Practice
Back
Next
Please complete to check your understanding.
Try it
Are the following similar figures?
Practice
Back
Next
Please complete to check your understanding.
Try it
Determine the series of transformations that get the preimage to the image. Then determine if the images are congruent or similar.
Click the button to reveal the answer.
Practice
Back
Next
Please complete to check your understanding.
Try it
Determine the series of transformations that get the preimage to the image. Then determine if the images are congruent or similar.
Click the button to reveal the answer.
Practice
Back
Next
Please complete to check your understanding.
Try it
Are the following similar or congruent figures?
Practice
Back
Next
Please complete to check your understanding.
Try it
Are the following similar or congruent figures?
Practice
Back
Next
Please complete to check your understanding.
Try it
Are the following similar or congruent figures?
Attributions
Back
Brigban, CC0, via Wikimedia Commons
Hawesthoughts, CC0, via Wikimedia Commons
“Virtual Manipulatives.” Polypad, polypad.amplify.com/p#algebra-tiles. Accessed 05-06 Feb. 2024.
Remember Scale Factor
Scale factor is the ratio between the length of each original side length and its corresponding dilated side length.
2x
The scale factor in this example is 2 because all scale length have been multiplied by 2.
2x
2x
Rotation
Rotations will always yield congruent figures because the rotation will turn the image around in a circle, changing their location and orientation not their shape or size.
ABC≅A'B'C'
The preiamge was translated by 2 units to the right and 2 units down. Then reflected over the x-axis. They are congruent because all transformations used were rigid.
Translation
Translations will always yield congruent figures because the translation will slide across the page, changing their location not their shape or size.
ABC≅A'B'C'
Reflection
Reflections will always yield congruent figures because the reflection will flip the image over a line of reflection, changing orientation not their shape or size.
ABCD≅A'B'C'D'
A preimage is the original object or set of points before a transformation is applied to it.
Preimage
A figure refers to a geometric shape. It's a combination of points, lines, or planes that form a closed boundary. The shapes can be 3-Dimensional or flat shapes.
Examples:
The preimage is dilated by a scale factor of 2. The images are similar figures because a dilation was used and dilations are not rigid.
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Transcript
Similar Figures
Next
Define Similar Figures:
- Understand the definition of similar figures and how they differ from congruent figures.
- Identify the symbol used to denote similarity (~).
Recognize Properties of Similar Figures:- Describe the properties of similar figures, emphasizing that they have the same shape but different sizes.
- Understand that corresponding angles in similar figures are equal, and corresponding sides are proportional.
Understand Transformations Leading to Similarity:these text boxes
In this lesson click to show more information.
Review
Back
Next
Congruent figures are ____ that are exactly the same shape and size. The symbol to show congruence is ≅.
figures
Rigid Transformations are transformations that change orientation but do not change shape or size. Rigid transformations will always yield congruent figures.
Translation
Reflection
Rotation
Similar Figures
Back
Next
rigid transformations
We know that when one or more ____________________ occur, the ________ and the image are congruent. But, we have one more transformation, dilation, which is not rigid.
preimage
When a dilation occurs, the preimage and image are similar. Similar figures are figures that have the same shape but different sizes. The symbol to show similarity is ~.
Similar Figures
Back
Next
Below is an example of a similar figure:
Scale Factor
What do notice about the side lengths? What do you notice about the angles?
Info
Info
Practice
Back
Next
Please complete to check your understanding.
Try it
Are the following similar figures?
Practice
Back
Next
Please complete to check your understanding.
Try it
Are the following similar figures?
Practice
Back
Next
Please complete to check your understanding.
Try it
Are the following similar figures?
Practice
Back
Next
Please complete to check your understanding.
Try it
Determine the series of transformations that get the preimage to the image. Then determine if the images are congruent or similar.
Click the button to reveal the answer.
Practice
Back
Next
Please complete to check your understanding.
Try it
Determine the series of transformations that get the preimage to the image. Then determine if the images are congruent or similar.
Click the button to reveal the answer.
Practice
Back
Next
Please complete to check your understanding.
Try it
Are the following similar or congruent figures?
Practice
Back
Next
Please complete to check your understanding.
Try it
Are the following similar or congruent figures?
Practice
Back
Next
Please complete to check your understanding.
Try it
Are the following similar or congruent figures?
Attributions
Back
Brigban, CC0, via Wikimedia Commons
Hawesthoughts, CC0, via Wikimedia Commons
“Virtual Manipulatives.” Polypad, polypad.amplify.com/p#algebra-tiles. Accessed 05-06 Feb. 2024.
Remember Scale Factor
Scale factor is the ratio between the length of each original side length and its corresponding dilated side length.
2x
The scale factor in this example is 2 because all scale length have been multiplied by 2.
2x
2x
Rotation
Rotations will always yield congruent figures because the rotation will turn the image around in a circle, changing their location and orientation not their shape or size.
ABC≅A'B'C'
The preiamge was translated by 2 units to the right and 2 units down. Then reflected over the x-axis. They are congruent because all transformations used were rigid.
Translation
Translations will always yield congruent figures because the translation will slide across the page, changing their location not their shape or size.
ABC≅A'B'C'
Reflection
Reflections will always yield congruent figures because the reflection will flip the image over a line of reflection, changing orientation not their shape or size.
ABCD≅A'B'C'D'
A preimage is the original object or set of points before a transformation is applied to it.
Preimage
A figure refers to a geometric shape. It's a combination of points, lines, or planes that form a closed boundary. The shapes can be 3-Dimensional or flat shapes.
Examples:
The preimage is dilated by a scale factor of 2. The images are similar figures because a dilation was used and dilations are not rigid.