What is a congruent translation?

Videos, examples, and solutions to help Grade 8 students understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

Common Core: 8.G.2

Suggested Learning Targets

I can define congruency
I can identify symbols for congruency
I can apply the concept of congruency to write congruent statements.
I can reason that a 2-D figure is congruent to another if the second can be obtained by a sequence of rotation, reflections, and translation.
I can describe the sequence of rotations, reflections, translations that exhibits the congruence between 2-D figures using words.

The following table shows examples of congruence and transformation of figures: translation, rotation, and reflection. Scroll down the page for more examples and solutions.

Congruence (8.G.2)
Two figures are congruent if you can translate, rotate, and/or reflect one shape to get the other.

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Congruence and Transformations Using congruence transformations, including translation, reflection, and rotation.

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Creating a congruent triangle by translation, rotation, reflection

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Congruence Using Transformations
This video demonstrates congruence using transformations.

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2-dimensional Figure is Congruent to another if it is obtained by the Transformations: translation, reflection, and rotation

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8.g.2
The Common Core State Standards (CCSS) videos are designed to support states, schools, and teachers in the implementation of the CCSS. Each video is an audiovisual resource that focuses on one or more specific standards and usually includes examples/illustrations geared to enhancing understanding. The intent of each content-focused video is to clarify the meaning of the individual standard rather than to be a guide on how to teach each standard although the examples can be adapted for instructional use.

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If one shape can become another using Turns, Flips and/or Slides, then the shapes are Congruent:

Rotation		Turn!
Reflection		Flip!
Translation		Slide!

After any of those transformations (turn, flip or slide),
the shape still has the same size, area, angles and line lengths.

Here are 3 examples of shapes that are Congruent:


Congruent (Rotated and Moved)	Congruent (Reflected and Moved)	Congruent (Reflected, Rotated and Moved)

Congruent or Similar?

The two shapes need to be the same size to be congruent.

When we need to resize one shape to make it the same as the other, the shapes are Similar.

When we ...		Then the shapes are ...
... only Rotate, Reflect and/or Translate
... also need to Resize

Congruent? Why such a funny word that basically means "equal"? Maybe because they are only "equal" when placed on top of each other. Anyway it comes from Latin congruere, "to agree". So the shapes "agree".

In mathematics, a congruent transformation (or congruence transformation) is:

Another term for an isometry; see congruence (geometry).
A transformation of the form A → PTAP, where A and P are square matrices, P is invertible, and PT denotes the transpose of P; see Matrix Congruence and congruence in linear algebra.

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