A triangle is specified by side lengths 2 cm, 4 cm, and 9 cm. Classify the construction as unique, more than one triangle, or impossible.
Show reasoning / computation: __________________________________________
CCSS 7.G.A.2 · unique, multiple, or no triangle
Triangle Construction: Unique, Multiple, or Impossible Worksheets
Classify whether given measurements determine one triangle, more than one triangle, or no triangle. The generator uses valid construction logic instead of decorative triangles that may contradict the measurements.
Preview · US Letter
Triangle Construction
Diagrams are part of the problem data, not decorative assets. Student pages keep solution-specific marks hidden; reveal answers or use the separate PDF key to check work.
Problem 1
Problem 2
A triangle is specified by side lengths 3 cm, 5 cm, and 11 cm. Classify the construction as unique, more than one triangle, or impossible.
Show reasoning / computation: __________________________________________
Problem 3
A triangle is specified by side lengths 7 cm, 8 cm, and 7 cm. Classify the construction as unique, more than one triangle, or impossible.
Show reasoning / computation: __________________________________________
Problem 4
A triangle is specified by angle measures 30°, 60°, and 90°. Classify the construction as unique, more than one triangle, or impossible.
Show reasoning / computation: __________________________________________
Problem 5
A triangle is specified by side lengths 3 cm, 2 cm, and 7 cm. Classify the construction as unique, more than one triangle, or impossible.
Show reasoning / computation: __________________________________________
Problem 6
A triangle is specified by side lengths 6 cm, 5 cm, and 13 cm. Classify the construction as unique, more than one triangle, or impossible.
Show reasoning / computation: __________________________________________
Problem 7
A triangle is specified by angle measures 45°, 70°, and 65°. Classify the construction as unique, more than one triangle, or impossible.
Show reasoning / computation: __________________________________________
Problem 8
A triangle is specified by side lengths 5 cm, 5 cm, and 10 cm. Classify the construction as unique, more than one triangle, or impossible.
Show reasoning / computation: __________________________________________
Teaching note 1
Three valid side lengths determine a unique triangle up to reflection.
Teaching note 2
Three angles can fix a triangle’s shape without fixing its size, so more than one similar triangle is possible.
Teaching note 3
If the two shorter sides do not total more than the longest side, no triangle can close.
Continue the 7.G progression
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Frequently asked questions
Do these require a compass and protractor?
They can be used as classification practice on their own; teachers can also have students construct selected items with drawing tools.
How do the worksheets show a 'more than one triangle' case?
AAA cases use three valid angle measures: the angles fix shape but not size, so multiple similar triangles satisfy the conditions.