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.
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| Questions Eliciting Thinking What do you know about similar triangles? How do their angles relate? How do their sides relate?
What characteristics of parallelogram ABCD might help you in this problem? How could the parallelogram help you?
Can you trace the two triangles you named and explain the parts that correspond or match-up between the two figures?
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 in 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 a scale of 3:1.
- Of a property of a parallelogram that the opposite angles are congruent.
- They are vertical triangles and similar by ASA.
When attempting to find the unknown lengths, the student:
- Writes proportions incorrectly.
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| 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? |
| 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 a proportion. 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 1 (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 FC, but does not provide sufficient justification of the similarity.
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| 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 identified. 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 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,
 .
- 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 shows appropriate work to find the value of x as  or 4 or 3.75.
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| Questions Eliciting Thinking Are there any other pairs of similar or congruent triangles in the diagram?
If two triangles are congruent, are they also similar?
Why did you choose not to use the other pair triangles for this problem? |
| Instructional Implications Challenge the student to find, name, and justify all pairs of similar or congruent triangles in the diagram.
Consider implementing MFAS tasks Similar Triangles 1 (G-SRT.2.5), Basketball Goal (G-SRT.2.5), County Fair (G-SRT.2.5) and Prove Rhombus Diagonals Bisect Angles (G-SRT.2.5). |
