ALEX Classroom Resource

  

Congruent vs Similar Triangles

  Classroom Resource Information  

Title:

 Congruent vs Similar Triangles

URL:

 https://aptv.pbslearningmedia.org/resource/mgbh-math-ee-gcongsim/congruent-vs-similar-triangles/

Content Source:

 PBS
Type: Audio/Video

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.

Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 7
Accelerated
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.

a. Given a pair of two-dimensional figures, determine if a series of rigid motions maps one figure onto the other, recognizing that if such a sequence exists the figures are congruent; describe the transformation sequence that verifies a congruence relationship. [Grade 8, 22]
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Confirm characteristics of the figures, such as lengths of line segments, angle measures and parallel lines as they develop a definition for congruent figures.
  • Use mathematical vocabulary to distinguish between a pair of congruent figures, noting that the figure prior to the transformation is called the preimage and the post-transformation figure is called the image.
  • Examine two figures to identify the rigid transformation(s) that produced the image from the pre-image. they can recognize the symbol for congruency (≅) and write statements of congruence.
Teacher 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.
Diverse Learning Needs:
Mathematics
MA2019 (2019)
Grade: 7
Accelerated
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
Evidence Of Student Attainment:
Students:
  • Explain how transformations can be used to prove that two figures are similar.
  • Describe a sequence of transformations to prove or disprove that two figures are similar or congruent.
Teacher 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.
Diverse Learning Needs:
Mathematics
MA2019 (2019)
Grade: 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.

a. Given a pair of two-dimensional figures, determine if a series of rigid motions maps one figure onto the other, recognizing that if such a sequence exists the figures are congruent; describe the transformation sequence that verifies a congruence relationship.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Confirm characteristics of the figures. such as lengths of line segments, angle measures, and parallel lines as they develop a definition for congruent figures.
  • Use mathematical vocabulary to distinguish between a pair of congruent figures, noting that the figure prior to the transformation is called the preimage and the post-transformation figure is called the image.
  • Examine two figures to identify the rigid transformation(s) that produced the image from the pre-image. they can recognize the symbol for congruency (≅) and write statements of congruence.
Teacher 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.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.8.22.1: Define rotation, reflection, and translation.
M.8.22.2: Recognize translations (slides), rotations (turns), and reflections (flips).
M.8.22.3: Distinguish between lines and line segments.
M.8.22.4: Demonstrate how to measure length.
M.8.22.5: Demonstrate how to use a protractor to measure angles.
M.8.22.6: Identify parallel lines.
M.8.22.7: Define congruent and sequence.
M.8.22.8: Compare translations to reflections.
M.8.22.9: Compare reflections to rotations.
M.8.22.10: Compare rotations to translations.
M.8.22.11: Identify attributes of two-dimensional figures.
M.8.22.12: Identify congruent figures.

Prior Knowledge Skills:
  • Define ordered pairs.
  • Name the pairs of integers and/or rational numbers of a point on a coordinate plane.
  • Demonstrate when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
  • Identify which signs indicate the location of a point in a coordinate plane.
  • Recall how to plot ordered pairs on a coordinate plane.
  • Define reflections.
  • Define reflections.
  • Calculate the distances between points having the same first or second coordinate using absolute value.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.8.22 Identify 3 different transformations (e.g., reflection, rotation, translation).
Mathematics
MA2019 (2019)
Grade: 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
Evidence Of Student Attainment:
Students:
  • Explain how transformations can be used to prove that two figures are similar.
  • Describe a sequence of transformations to prove or disprove that two figures are similar or congruent.
Teacher 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.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.8.24.1: Define similar.
M.8.24.2: Recognize dilations.
M.8.24.3: Recognize translations.
M.8.24.4: Recognize rotations.
M.8.24.5: Recognize reflections.
M.8.24.6: Identify similar figures.
M.8.24.7: Analyze an image and its dilation to determine if the two figures are similar.

Prior Knowledge Skills:
  • Define ordered pairs.
  • Name the pairs of integers and/or rational numbers of a point on a coordinate plane.
  • Demonstrate when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
  • Identify which signs indicate the location of a point in a coordinate plane.
  • Recall how to plot ordered pairs on a coordinate plane.
  • Define reflections.
  • Calculate the distances between points having the same first or second coordinate using absolute value.
Tags: congruent, congruent triangles, measurements, similar, similar triangles, triangle
License Type: Public Domain
For full descriptions of license types and a guide to usage, visit :
https://creativecommons.org/licenses
AccessibilityVideo resources: includes closed captioning or subtitles
Comments

This resource contains an activity to go with the video.

  This resource provided by:  
Author: Kristy Lacks
This site may contain links to other websites or content belonging to or originating from third parties or links to websites and features in banners or other advertising. Such external links are not investigated, monitored, or checked for accuracy, adequacy, validity, reliability, availability, or completeness by us. WE DO NOT WARRANT, ENDORSE, GUARANTEE, OR ASSUME RESPONSIBILITY FOR THE ACCURACY OR RELIABILITY OF ANY INFORMATION OFFERED BY THIRD-PARTY WEBSITES LINKED THROUGH THIS SITE.
Copyright © 2017, Alabama Learning Exchange
Alabama State Department of Education
Alabama State Department of Education