geometry topic 1 transformations and congruence

Topic 1Transformations and Congruence

Geometry

Odd : Tuesday 9/15/20Even: Wednesday 9/16/20

1.3: Representing and DescribingTransformations P. 31

Standards: MAFS.912.G-CO.1.2

Objectives:

• Describe transformations in the coordinate plane using algebraic representations and using words

Transformation – a change in the position, size, or shape of a figure. A transformation maps the preimage to the image.

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• A figure that is used as the input of a transformation is the preimage.

• The output is the image.

• Translations, reflections, and rotations are three types of transformations.

• The decorative tiles shown illustrate all three types of transformations.

➢ You can use prime notation to name the image of a point.➢ In the diagram, the transformation T moves point A to point A′ (read “A prime”).

❖ Coordinate notation is one way to write a rule for a transformation on a coordinate plane.❖ The notation uses an arrow to show how the transformation changes the coordinates of a general point, (x, y )

Coordinate Notation

The image and the preimage are congruent

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Find the unknown coordinates for each transformation and draw the image. Then complete the description of the transformation and compare the image to its preimage.

Reflection across the y-axis

The image and the preimage are congruent

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Find the unknown coordinates for each transformation and draw the image. Then complete the description of the transformation and compare the image to its preimage.

❖ Some transformations preserve length and angle measure, examples 1 & 2; and some do not, example 3.

❖ A rigid motion (or isometry) is a transformation that changes the position of a figure without changing the size or shape of the figure.

❖ Translations, reflections, and rotations are rigid motions.

Rigid motion– a transformation of the plane or space, which preserves distance and angles.

Properties of Rigid motion. P.33• Rigid motions preserve distance.• Rigid motions preserve angle measure.• Rigid motions preserve betweenness.• Rigid motions preserve collinearity.• Rigid motions preserve parallelism.

• If a figure is determined by certain points, then its image after a rigid motion is determined by the images of those points.

• This is true because of the betweenness and collinearity properties of rigid motions.• Rotations and translations also preserve orientation. This means that the order of the vertices of the

preimage and image are the same, either clockwise or counterclockwise.• Reflections do not preserve orientation.

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Your turn page 35

Your turn page 35

Practice

A

BC

DE

Practice Page 38

Practice Page 39

What term describes a transformation that does not change a figure’s size or shape?

A. SimilarityB. Rigid motion

C. Collinearity

D. Symmetry

MAFS.912.G-CO.1.2

The vertices of ∆𝐽𝐾𝐿 have coordinates J(5, 1), K(−2, −3), and L(−4, 1).

Under which transformation is ∆J ′K ′L ′ not congruent to ∆JKL?

A. A translation of two units to the right and two units down.

B. A counterclockwise rotation of 180 degrees around the origin.

C. A reflection over the x-axis.

D. A dilation with a scale factor of 2 and centered at the origin.

MAFS.912.G-CO.1.2

HOMEWORK

HMH online textbook:Homework 1.3

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