Congruent vs Similar Triangles

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.

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.

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.

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]

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.

Congruent vs Similar Triangles

Learning Resource Type

Subject Area

Grade(s)

Overview

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.

UP:MA19.8.22

Vocabulary

Knowledge

Skills

Understanding

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.

UP:MA19.8.24

Vocabulary

Knowledge

Skills

Understanding

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.

UP:MA19.7A.42

Vocabulary

Knowledge

Skills

Understanding

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]

UP:MA19.7A.44

Vocabulary

Knowledge

Skills

Understanding

CR Resource Type

Resource Provider

License Type

Comments or Notes

Approved Date

Congruent vs Similar Triangles

Learning Resource Type

Subject Area

Grade(s)

Overview

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.

Vocabulary

Knowledge

Skills

Understanding

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.

Vocabulary

Knowledge

Skills

Understanding

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.

Vocabulary

Knowledge

Skills

Understanding

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]

Vocabulary

Knowledge

Skills

Understanding

CR Resource Type

Resource Provider

License Type

URL (web address)

Comments or Notes

Approved Date

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.

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.

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.

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]