Triangle Inequality Flashcard

Front

Condition for three side lengths to form a triangle?

Back

The sum of any two lengths must be larger than the length of the third side.

Answer explanation

The condition for lengths to form a triangle is, when you add any two side lengths, the sum should be larger than the length of the third side. This ensures that the sides meet to form a triangle. If the sum were equal to or smaller, the sides would not meet, violating the triangle inequality principle.

Front

Which two sides can you test as a shortcut to determine if three side lengths can form a triangle?

Back

The two shortest sides

Answer explanation

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Hence, if the two shortest sides of a set of three lengths, when summed, are longer than the longest side, then a triangle can be formed.

Front

Can the side lengths 5, 4, and 2 form a triangle?

Back

Yes

Answer explanation

The side lengths of a triangle are given as 5, 4, and 2. The triangle inequality theorem states that the sum of the lengths of any two sides must be greater than the length of the remaining side. Here, 4+2=6 which is greater than 5. Hence, these lengths can form a triangle. The correct choice is 'Yes'.

Front

Can the side lengths 6, 1, and 7 form a triangle?

Back

No

Answer explanation

In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. This is known as the triangle inequality theorem. In this case, 6 + 1 = 7, which is not greater than 7. Therefore, the lengths 6, 1, and 7 cannot form a triangle.

Front

Can the side lengths 9, 8, and 2 form a triangle?

Back

Yes

Answer explanation

The provided lengths do not form a triangle. According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, 9 + 2 = 11, which is greater than 8; 8 + 2 = 10, which is greater than 9; but 9 + 8 = 17, which is not greater than 2. Therefore, it's not possible to form a triangle with these lengths.

Front

Sum of the two smallest sides of a triangle with side lengths 4, 6, and 5?

Back

9

Answer explanation

The sum of the two smallest sides of the triangle is calculated as follows: 4 + 5 = 9. This is the correct answer because in any triangle, the sum of lengths of any two sides should always be greater than the length of the third side. In this case, the two smallest sides are 4 and 5.

Front

Which of the following side lengths form a triangle? 1, 2, 3, 5, 7, 8, 6, 6, 14, 80, 20, 50

Back

5, 7, 8

Answer explanation

According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle always exceeds the length of the third side. Therefore, option '

5, 7, 8

' is the only set of side lengths that form a triangle, since 5+7 > 8, 5+8 > 7, and 7+8 > 5.

Front

The _________________ states that the sum of any two sides of a triangle must be greater than the third side.

Back

Inequality Theorem

Answer explanation

The correct answer is the Inequality Theorem. This theorem states that the sum of any two sides of a triangle must be greater than the third side. The question was asking about this specific property of triangles, which is not defined by the Equality Theorem, Theorem of Triangles, or the Angle Sum Theorem.