Grade 7 Math Practice Test: Triangle Inequality and Drawing Triangles from Given Conditions
- Triangle Inequality and Drawing Triangles
- 10 questions
- 15 minutes
This test covers the triangle inequality, the 180° angle sum and deciding whether given conditions make exactly one triangle, many triangles or none. Tip: for three side lengths, check only the two shorter sides; their sum must be greater than the longest side.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
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Question 1
Which set of side lengths, in centimeters, can form a triangle?
Correct answer: D
5 + 7 = 12 is greater than 10, so these sides close into a triangle. With 4, 5 and 9 the two short sides add up to exactly 9, so they lie flat on the long side and no triangle forms.
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Question 2
Two sides of a triangle measure 6 cm and 10 cm. Which could be the length of the third side?
Correct answer: A
The third side must be greater than 10 − 6 = 4 and less than 10 + 6 = 16. Only 12 cm is in that range; 4 cm and 16 cm are the boundary values and would not form a triangle.
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Question 3
Two sides of a triangle measure 8 inches and 13 inches. Which inequality describes all possible lengths x of the third side, in inches?
Correct answer: B
The third side must be longer than the difference 13 − 8 = 5 and shorter than the sum 13 + 8 = 21. The endpoints are not allowed, because a third side of exactly 5 or 21 makes a flat figure, so 5 ≤ x ≤ 21 is wrong.
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Question 4
Which set of angle measures can be the three angles of a triangle?
Correct answer: C
The angles of every triangle add up to 180°, and 35 + 65 + 80 = 180. The other sets add up to 190°, 170° and 190°.
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Question 5
Kim draws a triangle with angles of 50°, 60° and 70°. How many different triangles have exactly these angles?
Correct answer: D
The angles add up to 180°, so a triangle exists, but the angles fix only the shape. You can draw it small or large, so there are infinitely many such triangles, all scaled copies of each other.
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Question 6
How many different triangles can be drawn with side lengths of 5 cm, 6 cm and 7 cm?
Correct answer: C
The sides pass the triangle inequality (5 + 6 > 7), and three given side lengths fix the triangle completely. Any two such triangles are congruent, so there is exactly one.
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Question 7
Leo tries to build a triangle from three straws that are 3 cm, 4 cm and 9 cm long. What happens?
Correct answer: C
The two shorter straws together are only 3 + 4 = 7 cm, which is less than 9 cm, so their ends cannot meet. A triangle would need the sum of the two shorter sides to be greater than 9.
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Question 8
Which set of conditions determines exactly one triangle?
Correct answer: A
Two sides and the angle between them fix one triangle. Three angles fix only the shape (infinitely many sizes), 2 + 3 < 6 gives no triangle, and 100° + 85° is already more than 180°.
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Question 9
An isosceles triangle has one side of 4 cm and another side of 9 cm. What is its perimeter?
Correct answer: B
The two equal sides cannot both be 4 cm, because 4 + 4 < 9. So the sides are 9, 9 and 4 cm, and 9 + 9 + 4 = 22 cm. 17 cm uses the impossible sides 4, 4 and 9.
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Question 10
A triangle has sides of 7 m and 11 m. The third side is a whole number of meters. How many different lengths are possible for the third side?
Correct answer: D
The third side must be greater than 4 and less than 18, so it can be 5, 6, 7, …, 17. That is 17 − 5 + 1 = 13 lengths. 15 counts 4 and 18 as well, which do not work.
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