Congruent and Similar Triangles

 

This is one lesson in a larger Unit Plan that introduces triangular relationships through the lens of building a treehouse with a variety of triangular characteristics.  It has proofs, real world problems, constructions, a unit project, assessments, and more. In Lesson 19, “I'm Bored",  students use the conditions that make triangles congruent including SSS, AAA, SAS, ASA, AAS, and SSA, along with the conditions for Similarity SSS, and SAS, to complete the scale drawing and model of their treehouse. In addition they must use area formulas to determine the amount of materials needed to construct the the real world treehouse.    The entire unit plan can be found here. This lesson is part of the Unit Project. The project is group work, so it is easy to include differentiation. This is the truly hands-on part of the project as students finish their scale drawings and calculate materials. The rest of the project is found in lessons 3, 5, 8, 11, 15, & 20.

Standards & Objectives

Academic standards
CCSS.ELA-Literacy.RF.2.4
Read with sufficient accuracy and fluency to support comprehension.
CCSS.ELA-Literacy.RI.2.1
Ask and answer such questions as who, what, where, when, why, and how to demonstrate understanding of key details in a text.
CCSS.ELA-Literacy.RI.3.7
Use information gained from illustrations (e.g., maps, photographs) and the words in a text to demonstrate understanding of the text (e.g., where,...
CCSS.ELA-Literacy.RL.2.1
Ask and answer such questions as who, what, where, when, why, and how to demonstrate understanding of key details in a text.
CCSS.ELA-Literacy.RL.2.7
Use information gained from the illustrations and words in a print or digital text to demonstrate understanding of its characters, setting, or plot.
CCSS.ELA-Literacy.RL.3.7
Explain how specific aspects of a text's illustrations contribute to what is conveyed by the words in a story (e.g., create mood, emphasize...
CCSS.ELA-Literacy.SL.2.1
Participate in collaborative conversations with diverse partners about grade 2 topics and texts with peers and adults in small and larger groups.
CCSS.ELA-Literacy.SL.2.3
Ask and answer questions about what a speaker says in order to clarify comprehension, gather additional information, or deepen understanding of a...
CCSS.ELA-Literacy.SL.2.4
Tell a story or recount an experience with appropriate facts and relevant, descriptive details, speaking audibly in coherent sentences.
CCSS.ELA-Literacy.SL.3.1
Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 3 topics and...
CCSS.ELA-Literacy.SL.3.3
Ask and answer questions about information from a speaker, offering appropriate elaboration and detail.
CCSS.ELA-Literacy.SL.4.1
Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 4 topics and...
CCSS.ELA-Literacy.W.2.5
With guidance and support from adults and peers, focus on a topic and strengthen writing as needed by revising and editing.
CCSS.ELA-Literacy.W.2.7
Participate in shared research and writing projects (e.g., read a number of books on a single topic to produce a report; record science observations).
CCSS.ELA-Literacy.W.3.6
With guidance and support from adults, use technology to produce and publish writing (using keyboarding skills) as well as to interact and collaborate...
CLE 3108.4.2
Describe the properties of regular polygons, including comparative classification of them and special points and segments.
CLE 3108.4.4
Develop geometric intuition and visualization through performing geometric constructions with straightedge/compass and with technology.
CLE 3108.4.5
Extend the study of planar figures to three-dimensions, including the classical solid figures, and develop analysis through cross-sections.
CLE 3108.4.8
Establish processes for determining congruence and similarity of figures, especially as related to scale factor, contextual applications, and transformations.
GLE 0201.1.2
Employ a variety of strategies to decode words and expand vocabulary.
GLE 0201.2.1
Develop critical listening skills essential for comprehension, problem solving, and task completion.
GLE 0201.2.2
Develop critical speaking skills essential for effective communication.
GLE 0201.3.4
Revise first drafts for clearer meaning, correct capitalization, and punctuation.
GLE 0201.8.2
Employ a variety of basic reading comprehension strategies.
GLE 0201.8.3
Develop reading fluency and accuracy.
GLE 0301.2.1
Continue to develop basic listening skills necessary for communication.
GLE 0301.2.2
Continue to develop basic speaking skills necessary for communication.
GLE 0401.2.1
Continue to develop oral language skills necessary for communication.
GLE 0401.2.2
Continue to develop listening skills necessary for communication.
SPI 0301.6.4
Locate information using available text features (e.g., charts, maps, graphics).
SPI 0401.6.6
Use available text features (e.g., graphics and illustrations) to make meaning from text.
TSS.ELA.2.FL.F.5
Read with sufficient accuracy and fluency to support comprehension.
TSS.ELA.2.RI.IKI.8
Describe how reasons support specific points an author makes in a text.
TSS.ELA.2.RI.KID.1
Ask and answer such questions as who, what, where, when, why, and how to demonstrate understanding of key details in a text.
TSS.ELA.2.RL.KID.1
Ask and answer such questions as who, what, where, when, why, and how to demonstrate understanding of key details in a text.
TSS.ELA.2.SL.CC.1
Participate with varied peers and adults in collaborative conversations in small or large groups about appropriate 2nd grade topics and texts.
TSS.ELA.2.SL.CC.3
Ask and answer questions about what a speaker says in order to gather information or clarify something that is not understood.
TSS.ELA.2.SL.PKI.4
Tell a story or recount an experience with appropriate facts and relevant, descriptive details, speaking audibly in coherent sentences.
TSS.ELA.2.W.PDW.5
With guidance and support from adults, focus on a topic, respond to questions and suggestions from peers, and strengthen writing as needed by revising and...
TSS.ELA.2.W.RBPK.7
Participate in shared research and writing projects, such exploring a number of books on a single topic or engaging in science experiments to produce a report.
TSS.ELA.3.RI.IKI.7
Use information gained from illustrations and the words in a text to demonstrate understanding of a text.
TSS.ELA.3.RI.IKI.8
Explain how reasons support specific points an author makes in a text.
TSS.ELA.3.RL.IKI.7
Explain how illustrations in a text contribute to what is conveyed by the words.
TSS.ELA.3.SL.CC.1
Prepare for collaborative discussions on 3rd grade level topics and texts; engage effectively with varied partners, building on others' ideas and...
TSS.ELA.3.SL.CC.3
Ask and answer questions about information from a speaker, offering appropriate elaboration and detail.
TSS.ELA.3.W.PDW.6
With guidance and support from adults, use technology to produce and publish writing, as well as to interact and collaborate with others; demonstrate...
TSS.ELA.4.SL.CC.1
Prepare for collaborative discussions on 4th grade level topics and texts; engage effectively with varied partners, building on others' ideas and...
 
Alignment of this item to academic standards is based on recommendations from content creators, resource curators, and visitors to this website. It is the responsibility of each educator to verify that the materials are appropriate for your content area, aligned to current academic standards, and will be beneficial to your specific students.
 
Essential and guiding questions: 

From Lesson 16:

  • What are the differences and similarities between congruence and similarity?
  • When is being similar “good enough”?

From Lesson 17:

  • How are the theorems in this lesson connected?
  • Which of these theorems would appear to most useful in the real world?

From Lesson 18:

  • How are congruent triangles and similar triangles the same and different?
  • How are congruence relationships useful in everyday life?

Lesson Variations

Blooms taxonomy level: 
Understanding

Helpful Hints

Materials: 

  • pencil
  • paper
  • calculators for their scaled drawing
  • and any available resources that might be helpful in their construction of the scale model.

References

Contributors: