Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 64755
Similar Triangles - 1
Students are asked locate a pair of similar triangles in a diagram, explain why they are similar, and use the similarity to find two unknown lengths in
the diagram.
Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, similar triangles, proportions
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_SimilarTriangles1_Worksheet.docx
MFAS_SimilarTriangles1_Worksheet.pdf
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
This task can be implemented individually, with small groups, or with the whole class.
1. The teacher asks the student to complete the problems on the Similar Triangles - 1 worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student is not able to identify a pair of similar triangles in the diagram.
Examples of Student Work at this Level
The student names a pair of triangles that are either not similar or are similar but are not named in correct corresponding order. The student is not able to explain why the
triangles are similar and cannot write correct proportions to solve for the unknown lengths.
Questions Eliciting Thinking
Can you trace the two triangles you named and identify the corresponding parts?
What do you know about similar triangles? How do their angles relate? How do their sides relate?
page 1 of 4 What properties of parallelogram ABCD might help you in this problem?
Since the opposite sides of parallelogram ABCD are parallel, do you see a segment that could serve as a transversal? How might parallel segments cut by a transversal assist
you in identifying congruent angles?
Instructional Implications
Review ways to show two triangles are similar (AA, SAS, SSS) and what must be established using each method. Remind the student that once two triangles are
determined to be similar, all corresponding angles are congruent and all corresponding sides are proportional. Assist the student in locating and correctly naming a pair of
similar triangles. Model a clear and concise explanation of their similarity and challenge the student to find another pair of similar triangles in the diagram.
Review the definition of similarity and its consequences (i.e., corresponding angles of similar triangles are congruent and corresponding sides are proportional). Guide the
student to write and solve appropriate proportions to find x and y.
Provide additional opportunities to solve problems involving similar triangles and guide the student to write and solve proportions to find missing lengths.
Moving Forward
Misconception/Error
The student cannot adequately justify triangle similarity or use similarity to find unknown lengths.
Examples of Student Work at this Level
The students identifies a pair of similar triangles in the diagram and states the triangles are similar because:
They are on opposite sides of the transversal.
They share a side and have congruent angles.
Of the Triangle Proportionality Theorem (or “Side­Splitter” Theorem).
When attempting to find the unknown lengths, the student:
Writes proportions incorrectly.
Calculates a scale factor but uses it incorrectly.
page 2 of 4 Questions Eliciting Thinking
How can you show two triangles are similar? What theorems can be used?
What do you know about these two triangles? Will the properties of parallelogram ABCD help you show the triangles are similar?
What parts of the two similar triangles are you comparing in your proportion? Do these parts correspond?
How can your scale factor be used to find missing lengths?
Instructional Implications
Review ways to show two triangles are similar (AA, SAS, SSS) and what must be established using each method. Model a clear and concise explanation of the similarity of
the pair of triangles the student identifies. Challenge the student to find another pair of similar triangles in the diagram and to justify the similarity. Provide additional
opportunities for students to identify similar triangles and explain why they are similar.
Provide feedback to the student concerning any errors in writing or solving the proportions. Allow the student to revise his or her work.
If needed, provide more practice with solving proportions and give the student additional opportunities to solve problems involving similar triangles.
Consider implementing MFAS tasks Similar Triangles 2 (G-SRT.2.5), Basketball Goal (G-SRT.2.5) and County Fair (G-SRT.2.5).
Almost There
Misconception/Error
The student provides a correct response but with insufficient reasoning or imprecise language.
Examples of Student Work at this Level
The student names a pair of similar triangles and correctly solves for x and y but does not provide sufficient justification of the similarity.
Questions Eliciting Thinking
How can you show two triangles are similar? What theorems can be used?
What do you know about these two triangles? Will the properties of parallelogram ABCD help you show the triangles are similar?
Instructional Implications
Review ways to show two triangles are similar (AA, SAS, SSS) and what must be established using each method. Model a clear and concise explanation of the similarity of
the pair of triangles the student identifies. Challenge the student to find another pair of similar triangles in the diagram and to justify the similarity. Provide additional
opportunities for the student to identify similar triangles and explain why they are similar.
Consider implementing MFAS tasks Similar Triangles 2 (G-SRT.2.5), Basketball Goal (G-SRT.2.5) and County Fair (G-SRT.2.5).
Got It
Misconception/Error
The student provides complete and correct responses to all components of the task.
Examples of Student Work at this Level
The student:
Identifies a pair of similar triangles,
or
or
.
States the triangles are similar by the AA Similarity Theorem, identifies two pairs of corresponding congruent angles, and appropriately justifies each congruence.
Writes proportions such as
=
and
=
or
=
and
=
and shows appropriate work to find the value of x as
or 4
or 4.875 and the
page 3 of 4 value of y as
or 2
or 2.625.
Questions Eliciting Thinking
How many pairs of similar triangles can you find in this diagram?
Can you prove any of those pairs of triangles similar?
Instructional Implications
Challenge the student to find, name, and justify all pairs of similar triangles in the diagram.
Consider implementing MFAS tasks Similar Triangles 2 (G-SRT.2.5), Basketball Goal (G-SRT.2.5), County Fair (G-SRT.2.5) and Prove Rhombus Diagonals Bisect Angles (GSRT.2.5).
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Similar Triangles - 1 Worksheet
SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
District/Organization of Contributor(s): Okaloosa
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.912.G-SRT.2.5:
Description
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Remarks/Examples:
Geometry - Fluency Recommendations
Fluency with the triangle congruence and similarity criteria will help students throughout their investigations of
triangles, quadrilaterals, circles, parallelism, and trigonometric ratios. These criteria are necessary tools in many
geometric modeling tasks.
page 4 of 4