Triangle Inequalities Quiz

What does the triangle inequality theorem state about the sum of the lengths of any two sides of a triangle?

• It is equal to the length of the third side.

• It is twice the length of the third side.

• It is greater than the length of the third side.

• It is less than the length of the third side.

If one angle of a triangle is larger than another, what can be said about the sides opposite these angles?

• The side opposite the larger angle is shorter.

• The side opposite the larger angle is longer.

• The sides are equal.

• The side opposite the larger angle is the same as the other side.

What is the relationship between the sides of a triangle and its angles?

• The longest side is opposite the smallest angle.

• The longest side is opposite the largest angle.

• All sides are equal regardless of angles.

• The longest side is opposite the right angle.

Which segment is the shortest from a point to a line?

• A horizontal segment

• A parallel segment

• A perpendicular segment

• A diagonal segment

If two sides of a triangle are 6 and 7, can the third side be 11?

• No, because 6 + 7 is not equal to 11.

• No, because 6 + 7 is less than 11.

• Yes, because 6 + 7 is greater than 11.

• Yes, because 6 + 7 is equal to 11.

In triangle ABC, if angle A is the smallest, which side is the shortest?

• Side AB

• Side BC

• Side AC

• Side opposite angle A

What is the correct way to write the inequality for a triangle with sides 15, 13, and x?

• x < 28 or x > 2

• x < 28 and x > 2

• x > 28 and x < 2

• x = 28 or x = 2

In a triangle, if the side opposite the smallest angle is AB, what can be inferred about angle A?

• Angle A is a right angle.

• Angle A is the smallest angle.

• Angle A is equal to angle B.

• Angle A is the largest angle.

What is the range of possible values for X if the sides of a triangle are 3x + 21, 5x - 9, and 7x + 1?

• X is between 3 and 12

• X is between 5 and 20

• X is between 2 and 15

• X is between 1 and 10

Which property is used to prove that the sum of the sides of a quadrilateral is greater than twice one of its diagonals?

• Similarity theorem

• Congruence theorem

• Pythagorean theorem

• Triangle inequality theorem