Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Test the side lengths before you try to draw, add the angles to check for 180°, and think of the ruler and protractor steps. The last problems use realistic frames, trails and surveys.
Standards: 7.G.A.2 · Level: Grade 7
Problem 1 Three Poles, First Test ★★★
Can segments of 5 in, 6 in and 12 in form a triangle? Explain.
Problem 2 Three Poles, Second Test ★★★
Can segments of 7 in, 9 in and 12 in form a triangle? Explain.
Problem 3 Find the Third Angle ★★★
A triangle has angles of 48° and 67°. Find the third angle.
Problem 4 Which Set Works ★★★
Which set of lengths forms a triangle: (a) 8, 8, 15; (b) 6, 9, 16; (c) 10, 10, 20?
Problem 5 Range of the Third Side ★★★
Two sides of a triangle are 7 in and 11 in. Between which two numbers must the third side lie?
Problem 6 A Flat Triangle ★★★
Explain why sides of 6, 9 and 15 cannot make a triangle. Describe what happens when you try to draw it.
Problem 7 Count the Triangles ★★★
Decide whether each set of conditions gives exactly one triangle, more than one, or none: (a) angles 30°, 60°, 90°; (b) angles 70°, 80°, 50°; (c) sides 5 in and 7 in with a 55° angle between them; (d) sides 4 in, 4 in and 9 in.
Problem 8 ASA Conditions ★★★
A triangle has angles of 35° and 80° and the side between them is 6 in. Find the third angle and decide whether the triangle is unique.
Problem 9 Classify by Angles ★★★
A triangle has angles of 112° and 41°. Find the third angle and say whether the triangle is acute, right or obtuse.
Problem 10 Base of an Isosceles Triangle ★★★
An isosceles triangle has two sides of 9 in. Which whole-number lengths can the base have?
Problem 11 Longest Side Known ★★★
The longest side of a triangle is 14 in and another side is 6 in. Which whole-number lengths can the third side have?
Problem 12 Two Triangles from SSA ★★★
In triangle ACB, angle A = 30°, AC = 8 and BC = 5. The height from C to line AB is 4. Show that two triangles are possible and find both lengths of AB.
Problem 13 Same Angles, Different Sizes ★★★
Maya draws a triangle with angles of 50° and 60° and a side of 4 in between them. Zane draws one with the same two angles and a side of 8 in between them. Are the triangles identical? Explain.
Problem 14 Draw and Compare ★★★
Draw AB = 3 in with angle A = 40° and angle B = 65°. Find angle C and decide which side of the triangle is the longest.
Problem 15 Poles for a Tent Frame ★★★
A camp leader has poles of 9 ft, 12 ft and 21 ft. Can they form a triangular frame?
Problem 16 Roof Truss Beams ★★★
Two rafters of a roof truss are 10 ft and 14 ft. The tie beam is cut to a whole number of feet. How many different lengths can the tie beam have?
Problem 17 Hiking Triangle ★★★
A hiker walks 3 mi east, turns and walks 4.5 mi in a different direction, and then walks straight back to the start. What are the possible lengths of the walk back?
Problem 18 Sail Angles ★★★
A triangular sail has angles of 74° and 58°. Find the third angle and classify the triangle by its angles.
Problem 19 Stained Glass Piece ★★★
A glass cutter needs a triangle with angles 40° and 85° and a 5 in side between them. Find the third angle, say whether the piece is unique, and list the steps to draw it.
Problem 20 Surveyor and the Tree ★★★
A surveyor stands at A with a line AB. A tree at C is 10 ft from A, and angle A = 30°. The height of C above line AB is 5 ft. How many triangles ACB are possible when BC is 3 ft, 5 ft, 7 ft or 12 ft?
