Subjects

Geometry

Transformations

Congruence and Similarity

Eighth Grade Transformations Notes: Big Ideas Math Worksheets & Answer Key

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Eighth Grade Transformations Notes: Big Ideas Math Worksheets & Answer Key

sofi regueira

@sofiregueira

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Eighth grade transformations in mathematics cover essential concepts of geometric transformations, including translations, reflections, rotations, and dilations. This comprehensive guide explores these transformations, their properties, and applications in the coordinate plane, as well as the concepts of congruence and similarity.

• Translations involve sliding figures without rotation
• Reflections create mirror images across a line of reflection
• Rotations turn figures around a center point
• Dilations change the size of figures while preserving shape
• Congruent figures have the same size and shape
• Similar figures have the same shape but may differ in size

5/30/2023

346

k
2.1- Translations
A transformation changes a figure into another
figure. The new figure is called the image.
A translation is a transforma

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Reflections

Reflections, also known as flips, create mirror images of figures across a line of reflection.

Definition: A reflection is a transformation that flips a figure over a line to create a mirror image.

In the coordinate plane, reflections can be performed over the x-axis or y-axis:

Example:

Reflection over x-axis: (x, y) → (x, -y)

Reflection over y-axis: (x, y) → (-x, y)

Highlight: In a reflection, the original figure and its image are identical.

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Rotations

Rotations involve turning figures around a point called the center of rotation by a specific angle.

Definition: A rotation is a transformation that turns a figure around a fixed point by a certain angle.

In the coordinate plane, rotations about the origin follow specific rules:

Example:

90° counterclockwise: (x, y) → (-y, x)

180° rotation: (x, y) → (-x, -y)

270° counterclockwise: (x, y) → (y, -x)

Highlight: In a rotation, the original figure and its image are identical.

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Congruent Figures

Congruent figures have the same size and shape, and can be transformed into each other through rigid motions.

Definition: Rigid motions are transformations that preserve length and angle measure, including translations, reflections, and rotations.

Vocabulary: Congruent figures have congruent angles and congruent sides.

Example: In congruent triangles, corresponding sides and angles are equal.

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Dilations

Dilations change the size of figures while maintaining their shape, with respect to a center of dilation.

Definition: A dilation is a transformation that enlarges or reduces a figure with respect to a fixed point.

In the coordinate plane, dilations are performed by multiplying coordinates by a scale factor:

Example: (x, y) → (kx, ky)

Where k > 1 results in enlargement, and 0 < k < 1 results in reduction.

Highlight: In a dilation, the ratio of side lengths of the image to the original figure is equal to the scale factor.

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Similar Figures

Similar figures have the same shape but not necessarily the same size, and can be transformed into each other through similarity transformations.

Definition: A similarity transformation is a sequence of dilations and rigid motions.

Highlight: Corresponding angles of similar figures are congruent, and corresponding side lengths are proportional.

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Perimeters and Areas of Similar Figures

The relationship between perimeters and areas of similar figures is based on their scale factor.

Highlight: The ratio of perimeters of similar figures is equal to the ratio of their corresponding side lengths.

Example: For similar triangles ABC and DEF: Perimeter of ABC / Perimeter of DEF = AB/DE = BC/EF = AC/DF

Highlight: The ratio of areas of similar figures is equal to the square of the ratio of their corresponding side lengths.

Example: For similar triangles ABC and DEF: Area of ABC / Area of DEF = (AB/DE)² = (BC/EF)² = (AC/DF)²

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Translations

Translations are transformations where figures slide without turning. Every point moves the same distance and direction.

Definition: A translation is a transformation that slides a figure without rotating it.

In the coordinate plane, translations are performed by adding values to x and y coordinates:

Example: (x, y) → (x + a, y + b)

Where a represents horizontal movement and b represents vertical movement. Positive values indicate up/right translations, while negative values indicate down/left translations.

Highlight: In a translation, the original figure and its image are identical.

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Subjects

Geometry

Transformations

Congruence and Similarity

Eighth Grade Transformations Notes: Big Ideas Math Worksheets & Answer Key

sofi regueira

@sofiregueira

16 Followers

5/30/2023

346

9th/8th

Geometry

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Reflections

Reflections, also known as flips, create mirror images of figures across a line of reflection.

Definition: A reflection is a transformation that flips a figure over a line to create a mirror image.

In the coordinate plane, reflections can be performed over the x-axis or y-axis:

Example:

Reflection over x-axis: (x, y) → (x, -y)

Reflection over y-axis: (x, y) → (-x, y)

Highlight: In a reflection, the original figure and its image are identical.

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Rotations

Rotations involve turning figures around a point called the center of rotation by a specific angle.

Definition: A rotation is a transformation that turns a figure around a fixed point by a certain angle.

In the coordinate plane, rotations about the origin follow specific rules:

Example:

90° counterclockwise: (x, y) → (-y, x)

180° rotation: (x, y) → (-x, -y)

270° counterclockwise: (x, y) → (y, -x)

Highlight: In a rotation, the original figure and its image are identical.

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Congruent Figures

Congruent figures have the same size and shape, and can be transformed into each other through rigid motions.

Definition: Rigid motions are transformations that preserve length and angle measure, including translations, reflections, and rotations.

Vocabulary: Congruent figures have congruent angles and congruent sides.

Example: In congruent triangles, corresponding sides and angles are equal.

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Dilations

Dilations change the size of figures while maintaining their shape, with respect to a center of dilation.

Definition: A dilation is a transformation that enlarges or reduces a figure with respect to a fixed point.

In the coordinate plane, dilations are performed by multiplying coordinates by a scale factor:

Example: (x, y) → (kx, ky)

Where k > 1 results in enlargement, and 0 < k < 1 results in reduction.

Highlight: In a dilation, the ratio of side lengths of the image to the original figure is equal to the scale factor.

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Similar Figures

Similar figures have the same shape but not necessarily the same size, and can be transformed into each other through similarity transformations.

Definition: A similarity transformation is a sequence of dilations and rigid motions.

Highlight: Corresponding angles of similar figures are congruent, and corresponding side lengths are proportional.

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Perimeters and Areas of Similar Figures

The relationship between perimeters and areas of similar figures is based on their scale factor.

Highlight: The ratio of perimeters of similar figures is equal to the ratio of their corresponding side lengths.

Example: For similar triangles ABC and DEF: Perimeter of ABC / Perimeter of DEF = AB/DE = BC/EF = AC/DF

Highlight: The ratio of areas of similar figures is equal to the square of the ratio of their corresponding side lengths.

Example: For similar triangles ABC and DEF: Area of ABC / Area of DEF = (AB/DE)² = (BC/EF)² = (AC/DF)²

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Translations

Translations are transformations where figures slide without turning. Every point moves the same distance and direction.

Definition: A translation is a transformation that slides a figure without rotating it.

In the coordinate plane, translations are performed by adding values to x and y coordinates:

Example: (x, y) → (x + a, y + b)

Where a represents horizontal movement and b represents vertical movement. Positive values indicate up/right translations, while negative values indicate down/left translations.

Highlight: In a translation, the original figure and its image are identical.

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Download in

Google Play

Download in

App Store

4.9+

Average App Rating

15 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User