Grade 7 Constructing Triangles Test: 45 Minutes

Contents

Key takeaway: This grade 7 constructing triangles test fits a 45-minute class and splits 20 points across eight tasks. It checks the triangle inequality, angle sums, protractor reading, and the question of how many triangles a set of measurements allows. A separate key lists the scoring details.

Students show every sum, write answers with units, and explain their reasoning when asked. One question presents a classmate’s claim about side-side-angle, which tests deeper understanding. Another asks for the construction steps in order.

This 45-minute test checks Common Core standard 7.G.A.2 on drawing triangles from given conditions. It has eight questions worth 20 points in total. Show every sum, write final answers with units, and explain your reasoning where a question asks for it.

Test information

Grade: Grade 7
Chapter: Drawing Geometric Figures and Constructing Triangles
Common Core: 7.G.A.2
Time: 45 minutes
Total: 20 points (Question 1: 3 pts; Question 2: 2 pts; Question 3: 2 pts; Question 4: 2 pts; Question 5: 4 pts; Question 6: 2 pts; Question 7: 3 pts; Question 8: 2 pts)

Grade 7 Constructing Triangles Test: questions 1–5

1. Triangle inequality (3 points)

Tell whether each set of lengths (in cm) can be the sides of a triangle.

6, 9, 14 (1 point)
5, 7, 12 (1 point)
8, 8, 15 (1 point)

2. Third side (2 points)

Two sides of a triangle measure 8 in. and 11 in. The third side is a whole number of inches.

Find the smallest possible length. (1 point)
Find the largest possible length. (1 point)

3. Angle measures (2 points)

Two angles of a triangle measure \(48^{\circ}\) and \(77^{\circ}\). Find the third angle. (1 point)
Can a triangle have angles of \(38^{\circ}\), \(64^{\circ}\), and \(79^{\circ}\)? Explain. (1 point)

4. Protractor angle (2 points)

The side of an angle on the right lies on the 0 line of the protractor.

Angle on a protractor.

Find the measure of the angle. (1 point)
A triangle has this angle. Find the largest whole-number measure that another angle of the triangle can have. (1 point)

5. How many triangles? (4 points)

Tell whether each set of measurements gives exactly one triangle, more than one triangle, or no triangle.

Sides 5 cm, 6 cm, 7 cm (1 point)
Sides 3 cm, 4 cm, 8 cm (1 point)
Angles \(30^{\circ}\), \(70^{\circ}\), \(80^{\circ}\) (1 point)
Sides 5 cm and 8 cm with the \(40^{\circ}\) angle between them (1 point)

Grade 7 Constructing Triangles Test: questions 6–8

6. Side-side-angle (2 points)

Jamal draws triangle ABC with \(\angle A=40^{\circ}\), \(AC=9\text{ cm}\), and \(BC=6\text{ cm}\). He says that no other triangle has these measurements. Is he correct? Explain.

Jamal’s triangle.

7. Straws (3 points)

Sofia has straws that are 4 in., 6 in., and 11 in. long.

Can she form a triangle with these three straws? Explain. (1 point)
She cuts the 11 in. straw to a whole-number length. Find the smallest and largest lengths that let her form a triangle. (2 points)

8. Construction steps (2 points)

Triangle ABC has \(AB=7\text{ cm}\), \(AC=5\text{ cm}\), and \(\angle A=50^{\circ}\).

Sketch of the triangle.

List, in order, the steps to draw this triangle with a ruler and a protractor.

What is on the 7th grade constructing triangles test?

The opening question tests sets of lengths such as 6, 9, and 14, and 5, 7, and 12. Next, two sides of 8 and 11 inches ask for the smallest and largest whole-number third side. Another item gives angles of 48 and 77 degrees and asks for the third angle.

How should you pace a grade 7 constructing triangles test?

Aim for about three minutes on a short item and about five on a longer one. The four-point question on how many triangles is the heaviest, so start it with quick sketches. Use the last few minutes to recheck each sum.

How do you handle the straw and construction questions?

Sofia has straws of 4, 6, and 11 inches. Since 4 plus 6 is 10, which is less than 11, the straws cannot form a triangle. For the construction, list the order: draw AB at 7 centimeters, measure a 50-degree angle at A, and mark C at 5 centimeters along the new ray.

The third angle in the angle question is 55 degrees, because 48 plus 77 is 125 and 180 minus 125 is 55.

The protractor question puts one ray on the zero line at the right, so read the scale that starts at zero on that side. Check that your answer is acute or obtuse, as the picture suggests.

Review plan for the triangles test

Tonight, test six random sets of lengths and write the sum next to each. Tomorrow, practice drawing a triangle from two sides and an angle with a protractor. In the exam, circle the longest side first, so the inequality is quick to check.