7th Grade Drawing Triangles from Given Conditions Worksheet (PDF)

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

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

These 20 problems practice 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). They start with the basic skill, move to different kinds of numbers and multistep work, and end with six word problems set in everyday situations such as shopping, sports, and travel.

Show every step of your work, and use the answer key only after you have tried each problem.

Grade 7 · Common Core State Standards: 7.G.A.2

Triangle constructions worksheet: exercises 1 to 10

Exercise 1 – Check 3, 4, 5

Triangle with sides 3, 4, 5.

Can sides of length 3 in, 4 in, and 5 in form a triangle?

Exercise 2 – Check 2, 3, 7

Three sticks.

Can sides of length 2 in, 3 in, and 7 in form a triangle?

Exercise 3 – Exactly equal

Can sides of length 5 cm, 5 cm, and 10 cm form a triangle? Explain.

Exercise 4 – A right triangle?

Sides of 6 ft, 8 ft, and 10 ft form a triangle. Show that they satisfy the triangle inequality in all three ways.

Exercise 5 – Angles that fit

Angles of \(50^{\circ}\), \(60^{\circ}\), and \(70^{\circ}\) are given. Can they be the angles of a triangle? Is the triangle unique?

Exercise 6 – Angles that don't fit

Can \(90^{\circ}\), \(60^{\circ}\), and \(40^{\circ}\) be the angles of a triangle?

Exercise 7 – How many triangles?

How many different triangles (up to size and position) can be drawn with sides 4 in, 6 in, and 7 in?

Exercise 8 – Third angle

Angles 40, 60 and the unknown angle.

Two angles of a triangle measure \(40^{\circ}\) and \(60^{\circ}\). Find the third angle.

Exercise 9 – Range of the third side

Two sides of a triangle are 5 in and 8 in. Find the possible lengths of the third side.

Exercise 10 – Included angle

Draw a triangle with two sides of 4 in and the angle between them equal to \(60^{\circ}\). Find the other two angles and the third side.

Exercises 11 and up

Exercise 11 – Unique or not?

A triangle has angles \(35^{\circ}\) and \(65^{\circ}\) with a 5-inch side between them. Is the triangle unique? Find the third angle.

Exercise 12 – Isosceles perimeter

Equal sides of 6 and base 8.

An isosceles triangle has a base of 8 in and a perimeter of 20 in. Find the length of each equal side, and check that a triangle exists.

Exercise 13 – Describe the drawing

Describe, in steps, how to draw a triangle with sides 3 in, 4 in, and 5 in using a ruler and a compass.

Exercise 14 – Right isosceles

A triangle has angles \(90^{\circ}\), \(45^{\circ}\), and \(45^{\circ}\). Is it unique if no side is given? What single fact would make it unique?

Exercise 15 – Craft sticks

Liam’s sticks.

Liam has craft sticks of lengths 7 in, 3 in, and 10 in. Can he make a triangle? Explain.

Exercise 16 – Whole-number third side

Sofia has sticks of 6 in and 9 in. How many whole-number lengths could the third stick have so that a triangle forms?

Exercise 17 – Three towns

Three towns are 12 mi, 5 mi, and 8 mi apart. Can the towns be the corners of a triangle? Explain.

Exercise 18 – Roof truss

A roof truss is an isosceles triangle with two base angles of \(35^{\circ}\) each. Find the top angle.

Exercise 19 – Perimeter 30

A triangle has a perimeter of 30 in and two sides of 9 in and 12 in. Find the third side and check that a triangle exists.

Exercise 20 – Tent base

A tent has two sides of 5 ft. How many whole-number base lengths are possible?

Key facts behind this triangle constructions worksheet

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 worksheet

Work through the exercises in order: they go from simple to challenging. Write every step on paper, then compare with the solutions page and redo any exercise you missed the next day.

Download the triangle constructions worksheet as a PDF with the button below and keep it with your notes.

All Grade 7 chapters: Grade 7 math.

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