Key takeaway: This grade 7 constructing triangles worksheet offers 20 printable problems on drawing triangles from given conditions. A separate answer key is available once students finish. The tasks follow standard 7.G.A.2 and move from reading a protractor to counting how many triangles fit a description.
Early items test side lengths with the triangle inequality and angle measures with the 180-degree sum. Middle items ask for steps with a ruler and compass. Later items use sticks, campsites, a garden fence, and a pennant, so students must decide when a drawing is unique.
This worksheet gives 20 problems on drawing triangles from given conditions, aligned with Common Core standard 7.G.A.2. The first problems use a protractor, angle sums, and the triangle inequality to test side lengths and angle measures.
The middle problems ask how many triangles fit a set of measurements: exactly one, more than one, or none. The last six are word problems with sticks, trails, gardens, surveys, banners, and a compass. Check each answer against the conditions.
Grade 7 Constructing Triangles Worksheet: problems 1–5
1. Reading a protractor
Maya places a protractor on an angle. One side of the angle lies on the 0 line at the right. Find the measure of the angle.
2. Triangle inequality check
Tell whether each set of lengths (in inches) can be the sides of a triangle.
- 3, 4, 5
- 2, 3, 6
- 5, 5, 10
- 7, 8, 12
3. Third angle and type
Two angles of triangle ABC measure \(48^{\circ}\) and \(67^{\circ}\), as shown. (a) Find the measure of angle C. (b) Classify the triangle as acute, right, or obtuse.
4. Angles of a triangle
Tell whether each set of angle measures can be the three angles of a triangle.
- \(50^{\circ}\), \(60^{\circ}\), \(70^{\circ}\)
- \(90^{\circ}\), \(60^{\circ}\), \(40^{\circ}\)
- \(100^{\circ}\), \(45^{\circ}\), \(35^{\circ}\)
- \(62^{\circ}\), \(59^{\circ}\), \(58^{\circ}\)
5. Decimal side lengths
Tell whether each set of lengths (in centimeters) can be the sides of a triangle. Show the sum of the two shorter sides.
- 1.5, 2.5, 4
- 2.5, 4, 6
- 3.2, 3.2, 6.3
- 0.8, 1.1, 2
Grade 7 Constructing Triangles Worksheet: problems 6–10
6. Third side length
Two sides of a triangle measure 5 in. and 9 in. Find the smallest and largest whole-number lengths for the third side.
7. Isosceles bases
An isosceles triangle has two sides that are each 7 in. long. The third side, the base, is a whole number of inches. (a) Find the smallest and largest possible bases. (b) How many different whole-number bases are possible?
8. Angles x, 2x, and 3x
The three angles of a triangle measure \(x^{\circ}\), \(2x^{\circ}\), and \(3x^{\circ}\). Find \(x\) and each angle, then classify the triangle as acute, right, or obtuse.
9. Three angles
Both triangles below have angles of \(35^{\circ}\), \(65^{\circ}\), and \(80^{\circ}\).
- Are the two triangles the same size?
- Do three angles always determine one triangle? Explain.
10. Equilateral triangle construction
Draw segment AB that is 5 cm long. Set a compass to 5 cm, draw an arc from A and an arc from B, and mark C where the arcs cross, as shown. Then draw AC and BC. (a) Find the lengths of AC and BC. (b) Measure the angles with a protractor. (c) Could a classmate follow the same steps and draw a different triangle?
Grade 7 Constructing Triangles Worksheet: problems 11–15
11. Two sides and an angle between
Jamal draws triangle ABC with \(AB=7\text{ cm}\), \(AC=5\text{ cm}\), and \(\angle A=40^{\circ}\). Sofia draws her own triangle with the same three measurements. Will the two triangles have the same size and shape? Explain.
12. Right angle between two sides
Draw an angle A of \(90^{\circ}\). Mark B on one ray so that AB = 6 cm and C on the other ray so that AC = 8 cm. Connect B and C, as shown. (a) Measure BC with a ruler. (b) Would every classmate who uses these three measurements get a triangle with the same size and shape? (c) Classify the triangle by its sides.
13. One, many, or none
Tell whether each set of measurements gives exactly one triangle, more than one triangle, or no triangle.
- Sides 4 cm, 5 cm, 6 cm
- Sides 3 in., 4 in., 8 in.
- Angles \(20^{\circ}\), \(70^{\circ}\), \(90^{\circ}\) (no side lengths)
- \(\angle A = 80^{\circ}\), \(\angle B = 35^{\circ}\), and AB = 5 cm
- Angles \(100^{\circ}\), \(90^{\circ}\), \(10^{\circ}\)
14. Two angles and a side
A triangle has \(\angle A=35^{\circ}\), \(\angle B=75^{\circ}\), and \(AB=8\text{ cm}\).
- Find the measure of \(\angle C\).
- How many different triangles have these measurements?
15. Stick triangle
Ethan has two sticks that are 7 in. and 10 in. long. A third stick is 18 in. long.
- Can the three sticks form a triangle? Explain.
- Ethan saws the 18 in. stick down to a whole-number length. Find the smallest and largest lengths that let the sticks form a triangle.
Grade 7 Constructing Triangles Worksheet: problems 16–20
16. Hiking loop
Three campsites A, B, and C form a triangular hiking loop. The trail from A to B is 5 miles and the trail from B to C is 8 miles. The ranger plans a straight trail from C back to A that is a whole number of miles. (a) Find the possible lengths of the trail from C to A. (b) Find the shortest and longest possible loops. (c) Aisha wants a loop of exactly 20 miles. Can the ranger build it? If so, how long is CA?
17. Garden fence
Priya plans a triangular garden. Two sides measure 40 ft and 25 ft. The third side is a whole number of feet.
- Write the possible lengths of the third side.
- Find the smallest and largest possible perimeters of the garden.
18. Land survey
A surveyor stands at post A and post B, which are 120 ft apart. The angle at A to a tree T is \(52^{\circ}\) and the angle at B to the same tree is \(71^{\circ}\). (a) Find the angle at the tree. (b) How many different triangles ATB match these measurements? (c) A helper says the angle at the tree is \(60^{\circ}\). Explain how you know the helper is wrong.
19. Pennant banner
Maya makes a triangular pennant. The base is 12 in. and the other two sides are equal, each a whole number of inches s. (a) Jamal says s = 6 works. Explain why it does not. (b) Find the smallest whole-number value of s. (c) Find the least possible perimeter.
20. Two possible triangles
Diego draws a \(30^{\circ}\) angle at A and marks C 10 cm from A on one ray. He sets a compass to 7 cm, puts the point on C, and swings an arc across the other ray. The arc crosses the ray in two places, \(B_1\) and \(B_2\), as shown.
- How many different triangles can Diego make?
- Which triangle has the longer side AB?
- Does side-side-angle always give exactly one triangle? Explain.
What do the first 7th grade triangle problems ask?
Maya places a protractor on an angle, and students read the measure from the correct scale. Then four sets of lengths, 3, 4, 5, then 2, 3, 6, then 5, 5, 10, and finally 7, 8, 12, are tested against the inequality. Only the first and last sets can form a triangle.
How do you solve a grade 7 constructing triangles worksheet missing side problem?
Two sides of 5 and 9 inches leave a range for the third side. It must be more than the difference, 4, and less than the sum, 14. So the whole-number choices run from 5 to 13. An isosceles triangle with two sides of 7 inches has base lengths from 1 to 13.
What about angles x, 2x, and 3x?
Add the three angles and set the total equal to 180. Then 6x equals 180, so x is 30. The angles are 30, 60, and 90 degrees, which makes the triangle a right triangle. Check by adding them again.
How do the word problems apply these rules?
Ethan has sticks of 7 and 10 inches and a third stick of 18 inches. Because 7 plus 10 is only 17, the sticks cannot close. Priya’s garden has sides of 40 and 25 feet, so the third side lies between 16 and 64. Diego’s compass arc can cross a ray twice, which gives two triangles.
The hiking loop and land survey problems add distances and angles in a map setting. Sketch the three points first, then label each known side or angle. A surveyor with a baseline of 120 feet and two angles fixes the tree position exactly, since two angles and a side give one triangle.
Sharpen your construction skills
Use a ruler and compass to redo the equilateral triangle from the early problems on clean paper. Then compare your arcs with a classmate’s. If a protractor reading gave you trouble, practice with three angles that you draw yourself and then measure.
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Grade 7 Drawing Geometric Figures and Constructing Triangles worksheet
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