Learning Resource Type

Classroom Resource

Congruent vs Similar Triangles

Subject Area

Mathematics

Grade(s)

7, 8

Overview

Learn about the characteristics required for congruent or similar figures. This video focuses on the variety of ways you can use the side and angle measurements of two triangles to check for congruence and also briefly discusses how that differs from similar figures. This video was submitted through the Innovation Math Challenge, a contest open to professional and nonprofessional producers.

    Mathematics (2019) Grade(s): 8

    MA19.8.22

    Verify experimentally the properties of rigid motions (rotations, reflections, and translations): lines are taken to lines, and line segments are taken to line segments of the same length; angles are taken to angles of the same measure; and parallel lines are taken to parallel lines.

    Unpacked Content

    UP:MA19.8.22

    Vocabulary

    • Congruent
    • Rotation
    • Reflection
    • Translation

    Knowledge

    Students know:
    • How to measure line segments and angles.
    • That similar figures have congruent angles.
    • The definition/concept of what a figure does when it undergoes a rotation, reflection, and translation.
    • How to perform a translation, reflection, and rotation.

    Skills

    Students are able to:
    • verify by measuring and comparing lengths of a figure and its image that after a figure has been translated, reflected, or rotated its corresponding lines and line segments remain the same length.

    Understanding

    Students understand that:
    • congruent figures have the same shape and size.
    • Two figures in the plane are said to be congruent if there is a sequence of rigid motions that takes one figure onto the other.
    Mathematics (2019) Grade(s): 8

    MA19.8.24

    Given a pair of two-dimensional figures, determine if a series of dilations and rigid motions maps one figure onto the other, recognizing that if such a sequence exists the figures are similar; describe the transformation sequence that exhibits the similarity between them.

    Unpacked Content

    UP:MA19.8.24

    Vocabulary

    • Translation
    • Reflection
    • Rotation
    • Dilation
    • Scale factor

    Knowledge

    Students know:
    • How to perform rigid transformations and dilations graphically and algebraically (applying coordinate rules).
    • What makes figures similar and congruent.

    Skills

    Students are able to:
    • Use mathematical language to explain how transformations can be used to prove that two figures are similar or congruent.
    • Demonstrate/perform a series of transformations to prove or disprove that two figures are similar or congruent.

    Understanding

    Students understand that:
    • There is a proportional relationship between corresponding characteristics of the figures, such as lengths of line segments, and angle measures as they develop a definition for similarity between figures.
    • The coordinate plane can be used as tool because it gives a visual image of the relationship between the two figures.
    Mathematics (2019) Grade(s): 7 - Grade 7 Accelerated

    MA19.7A.42

    Verify experimentally the properties of rigid motions (rotations, reflections, and translations): lines are taken to lines, and line segments are taken to line segments of the same length; angles are taken to angles of the same measure; and parallel lines are taken to parallel lines.

    Unpacked Content

    UP:MA19.7A.42

    Vocabulary

    • Congruent
    • Rotation
    • Reflection
    • Translation

    Knowledge

    Students know:
    • how to measure line segments and angles
    • That similar figures have congruent angles.
    • The definition/concept of what a figure does when it undergoes a rotation, reflection, and translation.
    • how to perform a translation, reflection, and rotation.

    Skills

    Students are able to:
    • verify by measuring and comparing lengths of a figure and its image that after a figure has been translated, reflected, or rotated its corresponding lines and line segments remain the same length.

    Understanding

    Students understand that:
    • congruent figures have the same shape and size.
    • Two figures in the plane are said to be congruent if there is a sequence of rigid motions that takes one figure onto the other.
    Mathematics (2019) Grade(s): 7 - Grade 7 Accelerated

    MA19.7A.44

    Given a pair of two-dimensional figures, determine if a series of dilations and rigid motions maps one figure onto the other, recognizing that if such a sequence exists the figures are similar; describe the transformation sequence that exhibits the similarity between them. [Grade 8, 24]

    Unpacked Content

    UP:MA19.7A.44

    Vocabulary

    • Translation
    • Reflection
    • Rotation
    • Dilation
    • Scale factor

    Knowledge

    Students know:
    • how to perform rigid transformations and dilations graphically and algebraically (applying coordinate rules).
    • What makes figures similar and congruent.

    Skills

    Students are able to:
    • use mathematical language to explain how transformations can be used to prove that two figures are similar or congruent.
    • Demonstrate/perform a series of transformations to prove or disprove that two figures are similar or congruent.

    Understanding

    Students understand that:
    • there is a proportional relationship between corresponding characteristics of the figures, such as lengths of line segments, and angle measures as they develop a definition for similarity between figures.
    • The coordinate plane can be used as tool because it gives a visual image of the relationship between the two figures.
    Link to Resource

    CR Resource Type

    Audio/Video

    Resource Provider

    PBS
    Accessibility
    License

    License Type

    PD
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