Standard 2: Apply properties of transformations to describe congruence or similarity.

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General Information
Number: MA.912.GR.2
Title: Apply properties of transformations to describe congruence or similarity.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Grade: 912
Strand: Geometric Reasoning

Related Benchmarks

This cluster includes the following benchmarks.

Related Access Points

This cluster includes the following access points.

Access Points

MA.912.GR.2.AP.1a
Given a preimage and image, identify the transformation.
MA.912.GR.2.AP.1b
Select the algebraic coordinates that represent the transformation.
MA.912.GR.2.AP.2
Select a transformation that preserves distance.
MA.912.GR.2.AP.3
Identify a given sequence of transformations, that includes translations or reflections, that will map a given figure onto itself or onto another congruent figure.
MA.912.GR.2.AP.5
Given a geometric figure and a sequence of transformations, select the transformed figure on a coordinate plane.
MA.912.GR.2.AP.6
Use rigid transformations that includes translations or reflections to map one figure onto another to show that the two figures are congruent.
MA.912.GR.2.AP.8
Identify an appropriate transformation to map one figure onto another to show that the two figures are similar.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this topic.

Formative Assessments

Justifying HL Congruence:

Students are asked to use rigid motion to explain why the HL pattern of congruence ensures right triangle congruence.

Type: Formative Assessment

Dilation of a Line: Factor of Two:

Students are asked to graph the image of three points on a line after a dilation using a center not on the line and to generalize about dilations of lines when the line does not contain the center.

Type: Formative Assessment

Dilation of a Line: Factor of One Half:

Students are asked to graph the image of three points on a line after a dilation using a center not on the line and to generalize about dilations of lines when the line does not contain the center.

Type: Formative Assessment

Dilation of a Line Segment:

Students are asked to dilate a line segment and describe the relationship between the original segment and its image.

Type: Formative Assessment

Congruent Trapezoids:

Students will determine whether two given trapezoids are congruent.

Type: Formative Assessment

Justifying a Proof of the AA Similarity Theorem:

Students are asked to justify statements of a proof of the AA Similarity Theorem.

Type: Formative Assessment

Prove the AA Similarity Theorem:

Students will indicate a complete proof of the AA Theorem for triangle similarity.

Type: Formative Assessment

Reflect a Semicircle:

Students are asked to reflect a semicircle across a given line.

Type: Formative Assessment

Dilation of a Line: Center on the Line:

Students are asked to graph the image of two points on a line after a dilation using a center on the line and to generalize about dilations of lines when the line contains the center.

Type: Formative Assessment

Two Triangles:

Students are asked to describe the transformations that take one triangle onto another.

Type: Formative Assessment

Transform This:

Students are asked to translate and rotate a triangle in the coordinate plane and explain why the pre-image and image are congruent.

Type: Formative Assessment

Rotation of a Quadrilateral:

Students are asked to rotate a quadrilateral around a given point.

Type: Formative Assessment

Repeated Reflections and Rotations:

Students are asked to describe what happens to a triangle after repeated reflections and rotations.

Type: Formative Assessment

Indicate the Transformations:

Students are asked to describe the transformations that take one triangle onto another.

Type: Formative Assessment

Demonstrating Rotations:

Students are asked to rotate a quadrilateral 90 degrees clockwise.

Type: Formative Assessment

Similarity - 2:

Students are asked to describe a sequence of transformations to show that two polygons are similar.

Type: Formative Assessment

Similarity - 1:

Students are asked to describe a sequence of transformations to show that two polygons are similar.

Type: Formative Assessment

Similarity - 3:

Students are asked to describe a sequence of transformations that demonstrates two polygons are similar.

Type: Formative Assessment

Proving Similarity:

Students are asked to explain similarity in terms of transformations.

Type: Formative Assessment

Proving the Alternate Interior Angles Theorem:

In a diagram involving two parallel lines and a transversal, students are asked to use rigid motion to prove that alternate interior angles are congruent.

Type: Formative Assessment

Proving Congruence:

Students are asked to explain congruence in terms of rigid motions.

Type: Formative Assessment

Multistep Congruence:

Students are asked to describe a sequence of rigid motions to demonstrate the congruence of two polygons.

Type: Formative Assessment

Rigid Motion - 3:

Students are asked to describe a rigid motion to demonstrate two polygons are congruent.

Type: Formative Assessment

Rigid Motion - 2:

Students are asked to describe a rigid motion to demonstrate two polygons are congruent.

Type: Formative Assessment

Rigid Motion - 1:

Students are asked to describe a rigid motion to demonstrate that two polygons are congruent.

Type: Formative Assessment

Showing Triangles Congruent Using Rigid Motion:

Students are asked to use the definition of congruence in terms of rigid motion to show that two triangles are congruent in the coordinate plane.

Type: Formative Assessment

Proving Congruence Using Corresponding Parts:

Students are asked to prove two triangles congruent given that all pairs of corresponding sides and angles are congruent.

Type: Formative Assessment

Showing Similarity:

Students are asked to use the definition of similarity in terms of similarity transformations to determine whether or not two quadrilaterals are similar.

Type: Formative Assessment

The Consequences of Similarity:

Students are given the definition of similarity in terms of similarity transformations and are asked to explain how this definition ensures the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

Type: Formative Assessment

To Be or Not To Be Similar:

Students are asked to use the definition of similarity in terms of similarity transformations to determine whether or not two triangles are similar.

Type: Formative Assessment

Justifying SSS Congruence:

Students are asked to use rigid motion to explain why the SSS pattern of congruence ensures triangle congruence.

Type: Formative Assessment

Justifying SAS Congruence:

Students are asked to use rigid motion to explain why the SAS pattern of congruence ensures triangle congruence.

Type: Formative Assessment

Justifying ASA Congruence:

Students are asked to use rigid motion to explain why the ASA pattern of congruence ensures triangle congruence.

Type: Formative Assessment

Showing Congruence Using Corresponding Parts - 2:

Students are given two triangles in which all pairs of corresponding parts are congruent and are asked to use the definition of congruence in terms of rigid motion to show the triangles are congruent.

Type: Formative Assessment

Showing Congruence Using Corresponding Parts - 1:

Students are given two triangles in which all pairs of corresponding parts are congruent and are asked to use the definition of congruence in terms of rigid motion to show the triangles are congruent.

Type: Formative Assessment

Congruence Implies Congruent Corresponding Parts:

Students are given two congruent triangles and asked to determine the corresponding side lengths and angle measures and to use the definition of congruence in terms of rigid motion to justify their reasoning.

Type: Formative Assessment

Transformations And Functions:

Students are given examples of three transformations and are asked if each is a function.

Type: Formative Assessment

Comparing Transformations:

Students are asked to determine whether or not dilations and reflections preserve distance and angle measure.

Type: Formative Assessment

Demonstrating Translations:

Students are asked to translate a quadrilateral according to a given vector.

Type: Formative Assessment

Demonstrating Reflections:

Students are asked to reflect a quadrilateral across a given line.

Type: Formative Assessment

Original Student Tutorial

Home Transformations:

Learn to describe a sequence of transformations that will produce similar figures. This interactive tutorial will allow you to practice with rotations, translations, reflections, and dilations.

Type: Original Student Tutorial

Perspectives Video: Professional/Enthusiasts

All Circles Are Similar- Especially Circular Pizza!:

What better way to demonstrate that all circles are similar then to use pizzas! Gaines Street Pies explains how all pizza pies are similar through transformations.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

Reflections, Rotations, and Translations with Additive Printing:

Transform your understanding of 3D modeling when you learn about how shapes are manipulated to arrive at a final 3D printed form!

Type: Perspectives Video: Professional/Enthusiast

3D Modeling with 3D Shapes:

Complex 3D shapes are often created using simple 3D primitives! Tune in and shape up as you learn about this application of geometry!

Type: Perspectives Video: Professional/Enthusiast

Making Candy: Uniform Scaling:

Don't be a shrinking violet. Learn how uniform scaling is important for candy production.

Type: Perspectives Video: Professional/Enthusiast

Bacteriophage Geometry and Structure:

Viruses aren't alive but they still need to stay in shape! Learn more about the geometric forms of bacteriophages!

Type: Perspectives Video: Professional/Enthusiast

Text Resource

Math for Hungry Birds:

This informational text resource is intended to support reading in the content area. A new study indicates that the flying patterns of hunting albatrosses may resemble mathematical designs called fractals. This article describes the basics of fractals and why scientists think the albatross may hunt in such patterns. As it turns out, many animals may use math to find food!

Type: Text Resource

Student Resources

Vetted resources students can use to learn the concepts and skills in this topic.

Original Student Tutorial

Home Transformations:

Learn to describe a sequence of transformations that will produce similar figures. This interactive tutorial will allow you to practice with rotations, translations, reflections, and dilations.

Type: Original Student Tutorial

Perspectives Video: Professional/Enthusiast

Making Candy: Uniform Scaling:

Don't be a shrinking violet. Learn how uniform scaling is important for candy production.

Type: Perspectives Video: Professional/Enthusiast

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this topic.

Perspectives Video: Professional/Enthusiast

Making Candy: Uniform Scaling:

Don't be a shrinking violet. Learn how uniform scaling is important for candy production.

Type: Perspectives Video: Professional/Enthusiast