Exploring the Converse of the Pythagorean Theorem

What does the Triangle Inequality Theorem state?

• The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

• The sum of any two sides of a triangle must be less than the third side.

• The longest side of a triangle must be equal to the sum of the other two sides.

• The area of a triangle can be determined by the sum of its three sides.

How can you determine if a set of three lengths can form a triangle?

• By subtracting the shortest length from the sum of the other two.

• By ensuring the sum of any two lengths is greater than the third length.

• By ensuring each length is less than the sum of the other two.

• By adding all three lengths and dividing by two.

Which statement is true according to the Triangle Inequality Theorem?

• A triangle with sides 7, 8, and 15 inches cannot be formed.

• A triangle with sides 4, 5, and 6 inches can be formed.

• A triangle with sides 4, 5, and 6 inches cannot be formed.

• A triangle with sides 7, 8, and 15 inches can be formed.

What is the converse of the Pythagorean theorem used for?

• To calculate the area of a right triangle.

• To find the height of a triangle.

• To determine if a triangle is equilateral.

• To identify if a triangle is a right triangle based on its side lengths.

Which set of lengths forms a right triangle?

• 7 inches, 9 inches, and 12 inches.

• 5 inches, 12 inches, and 13 inches.

• 10 inches, 16 inches, and 14 inches.

• 3.6 inches, 10 inches, and 13 inches.

What does it mean if the square of the longest side of a triangle is equal to the sum of the squares of the other two sides?

• The triangle is equilateral.

• The triangle is obtuse.

• The triangle is a right triangle.

• The triangle is acute.

How do you determine if a triangle is obtuse using the Pythagorean theorem?

• If the square of the longest side is greater than the sum of the squares of the other two sides.

• If the square of the longest side is equal to the sum of the squares of the other two sides.

• If the square of the longest side is less than the sum of the squares of the other two sides.

• If the sum of the squares of the two shorter sides is equal to twice the square of the longest side.

What indicates that a triangle is acute?

• The sum of the squares of the two shorter sides is less than the square of the longest side.

• The square of the longest side is equal to the sum of the squares of the other two sides.

• The square of the longest side is less than the sum of the squares of the other two sides.

• The square of the longest side is greater than the sum of the squares of the other two sides.

If a triangle has sides of 10, 16, and 14 centimeters, what type of triangle is it?

• Equilateral triangle

• Acute triangle

• Obtuse triangle

• Right triangle

Using the Pythagorean theorem, how can you classify a triangle with sides 3.6, 10, and 13 inches?

• Acute triangle

• Isosceles triangle

• Right triangle

• Obtuse triangle