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Constructing Triangles Test – Grade 7 Math (Printable PDF)

Last updated: October 22, 2026 · Written by the Math Made Easy math teachers

Grade 7 Math Tests – Mathbot, the Math Made Easy robot coach, with free printable tests for Grade 7
Looking for a constructing triangles test? Then this Grade 7 test on Building Triangles from Sides and Angles checks the whole chapter, with points for each question. This test covers the triangle inequality, angle sums and the conditions that give one triangle, more than one or none. Show the sums or checks that support each answer. A ruler is allowed for figures, but no protractor drawing is required. Plan on 45 minutes for the 8 questions.

Standards: 7.G.A.2 · Level: Grade 7

Time: 45 minutes · 8 questions · Total: 20 points · Calculator: as allowed by your teacher

Question 1 Triangle Inequality Tests (2 points)

Decide whether each set of lengths can form a triangle. Justify with the triangle inequality.

  1. 8 in, 11 in, 18 in (1 point)
  2. 9 in, 12 in, 21 in (1 point)

Question 2 Range of a Side (2 points)

Two sides of a triangle are 6 in and 15 in. Find the possible lengths of the third side.

Question 3 Third Angle (2 points)

A triangle has angles of 58° and 77°. Find the third angle and classify the triangle as acute, right or obtuse.

Question 4 Count the Triangles (3 points)

For each set of conditions, state whether exactly one triangle, more than one triangle or no triangle can be drawn.

  1. Sides of 7 in, 10 in and 12 in (1 point)
  2. Angles of 45°, 45° and 90° (1 point)
  3. Sides of 3 in, 5 in and 9 in (1 point)

Question 5 Triangle ABC (3 points)

Triangle ABC is drawn with a ruler and protractor.

A50°4 inB60°C
Triangle ABC.
  1. Find angle C. (1 point)
  2. Name the longest side and the shortest side. (1 point)
  3. Is this triangle unique? Explain. (1 point)

Question 6 Surveyor Problem (3 points)

In triangle ACB, angle A = 30° and AC = 10 in. The height of C above line AB is 5 in, as shown.

AC30°105
Angle A = 30°, AC = 10 in, and the height of C above line AB is 5 in.

How many different triangles ACB can be drawn if BC is:

  1. 4 in (1 point)
  2. 5 in (1 point)
  3. 8 in (1 point)

Question 7 Straw Triangle (3 points)

Two straws have lengths 7 in and 9 in. A third straw has length x in.

  1. Write the range of values of x that forms a triangle. (1 point)
  2. How many whole-number lengths of x work? (1 point)
  3. Explain why x = 16 does not work. (1 point)

Question 8 Find the Flaw (2 points)

Tara says, “Any three angles that add to 180° make exactly one triangle.”

  1. Give two different triangles that have the same three angles. (1 point)
  2. Explain why Tara is wrong. (1 point)

View the Constructing Triangles test answer key with scoring

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