7th Grade Drawing Triangles from Given Conditions Test with Point Values (PDF)

7th Grade math test: Drawing Triangles from Given Conditions – Maths PDF

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This triangle constructions test for 7th Grade covers drawing triangles from given conditions (Common Core 7.G.A.2), with a free PDF to print.

This 45-minute test checks drawing triangles from given side lengths and angle measures, the triangle inequality, and when conditions give one triangle, many triangles, or none (Common Core 7.G.A.2). It has 9 questions worth 20 points in all. Show your work, because most questions give partial credit for correct steps.

Time and points

About this test

Grade: Grade 7
Chapter: Drawing Triangles from Given Conditions
Standards: 7.G.A.2
Time: 45 minutes
Total: 20 points

Triangle constructions test: questions

Question 1 – Triangle inequality [2 pts]

Three sets of lengths.

Decide which sets can form a triangle. Show the check for each.

Question 2 – Angle sum [2 pts]

Can angles of \(72^{\circ}\), \(68^{\circ}\), and \(40^{\circ}\) form a triangle? If a fourth set has angles \(55^{\circ}\) and \(75^{\circ}\), find its third angle.

Question 3 – How many triangles? [2 pts]

For each description, tell whether it gives exactly one triangle, more than one, or none. (a) Sides 5, 6, 7. (b) Angles 30, 60, 90 only. (c) Sides 3, 3, 9.

Question 4 – Perimeter and range [2 pts]

A triangle drawn with a ruler.

Find the perimeter of the triangle. Then find the range of possible lengths for the third side of a different triangle with sides 4 in and 5 in.

Question 5 – Included angle [2 pts]

Describe how to draw a triangle with sides of 5 cm and 7 cm and an angle of \(40^{\circ}\) between them. Is the triangle unique?

Question 6 – Isosceles angles [2 pts]

An isosceles triangle.

Find the unknown angle, and tell whether the triangle is unique if no sides are given.

Question 7 – Whole-number sides [2 pts]

Two sides of a triangle are 8 in and 11 in. How many whole-number lengths are possible for the third side?

Question 8 – Stick kit [3 pts]

Sticks in Maya’s kit.

Can Maya make a triangle with the sticks 9 in, 4 in, and 6 in? (1 point)
She replaces the 4-inch stick by a 2-inch stick. Can she now make a triangle? (1 point)
Find the shortest whole-number stick that works with 9 in and 6 in. (1 point)

Question 9 – Kite frame [3 pts]

A kite frame.

Check that the sides 10 in, 10 in, and 15 in make a triangle. (1 point)
Find the perimeter. (1 point)
The base is changed to 20 in. Can a triangle still be made? Explain. (1 point)

Key facts behind this triangle constructions test

Key facts

Triangle inequality: the sum of any two sides is greater than the third side.
The angles of a triangle add up to \(180^{\circ}\).
Three fitting side lengths determine exactly one triangle.
Three angles alone give many triangles of different sizes.
Two sides and the angle between them determine exactly one triangle.

How to use this triangle constructions test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Grade 7 chapters: Grade 7 math.

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