Constructing Triangles Test Answer Key with Scoring – Grade 7

Question 1 Triangle Inequality Tests (2 points)

1. 8 + 11 = 19 > 18, and the other sums are larger: yes.
2. 9 + 12 = 21, which is not greater than 21: no.

Scoring: 1 point per part, for the correct answer with the sum shown.

Question 2 Range of a Side (2 points)

The third side is less than 6 + 15 = 21 and greater than 15 − 6 = 9.

Greater than 9 in and less than 21 in

Scoring: 1 point for each bound.

Question 3 Third Angle (2 points)

58 + 77 = 135, and 180 − 135 = 45. All angles (58°, 77°, 45°) are less than 90°.

45°; acute

Scoring: 1 point for the angle, 1 point for the classification.

Question 4 Count the Triangles (3 points)

1. 7 + 10 = 17 > 12: exactly one triangle (SSS).
2. No side is given, so more than one triangle (infinitely many).
3. 3 + 5 = 8 < 9: no triangle.

Scoring: 1 point per part.

Question 5 Triangle ABC (3 points)

1. Angle C = 180 − 50 − 60 = 70°.
2. The largest angle is C = 70°, opposite AB, so the longest side is AB. The smallest angle is A = 50°, opposite BC, so the shortest side is BC.
3. Yes. Two angles and the side between them (ASA) give exactly one triangle.

Scoring: 1 point per part.

Question 6 Surveyor Problem (3 points)

1. 4 < 5, so BC is shorter than the height: no triangle.
2. 5 equals the height: exactly one triangle (a right angle at the foot).
3. 5 < 8 < 10, so BC lies between the height and AC: two triangles.

Scoring: 1 point per part.

Question 7 Straw Triangle (3 points)

1. 9 − 7 < x < 9 + 7, so 2 < x < 16.
2. The whole numbers 3 through 15: 15 − 3 + 1 = 13.
3. 7 + 9 = 16, which is not greater than 16, so the straws lie flat.

Scoring: 1 point per part.

Question 8 Find the Flaw (2 points)

1. For example, a triangle with angles 30°, 60°, 90° and short sides 3 in, 5.2 in, 6 in, and another with the same angles and sides twice as long.
2. Angles fix the shape but not the size, so many triangles share the same three angles.

Scoring: 1 point per part.