Exploring the Pythagorean Theorem Converse

What is the main goal of using the converse of the Pythagorean theorem?

• To determine if a triangle is a right triangle

• To find the hypotenuse of a triangle

• To prove the Pythagorean theorem

• To calculate the area of a triangle

What does the converse of the Pythagorean theorem state?

• If the sum of the squares of two sides equals the square of the third side, the triangle is right

• The sum of the angles in a triangle is 180 degrees

• The longest side of a triangle is always the hypotenuse

• a^2 + b^2 = c^2 indicates a right triangle

In the example problem, why was the triangle not considered a right triangle?

• Because the sides were not squared correctly

• Because 200 does not equal 256

• Because the triangle had equal sides

• Because 200 equals 256

For a triangle with sides 12 cm, 16 cm, and 20 cm, is it a right triangle?

• Only if it's an isosceles triangle

• Insufficient information

• No

• Yes

For a triangle with sides 6 inches, 14 inches, and 19 inches, is it a right triangle?

• Only if it's an equilateral triangle

• Maybe

• No

• Yes

For a triangle with sides 40 mm, 75 mm, and 85 mm, is it a right triangle?

• Insufficient information

• No

• Only if it's a scalene triangle

• Yes

For a triangle with sides 77 miles, 83 miles, and 36 miles, is it a right triangle?

• Only if it's an obtuse triangle

• Yes

• No

• Maybe

For a triangle with sides 70 km, 74 km, and 24 km, is it a right triangle?

• Yes

• No

• Only if it's an acute triangle

• Insufficient information

For a triangle with sides 18 meters, 24 meters, and 30 meters, is it a right triangle?

• Yes

• Only if it's a right isosceles triangle

• Maybe

• No

What should you do before solving to determine if a triangle is right using the converse of the Pythagorean theorem?

• Square the longest side only

• Add all sides together

• Put the sides in order from shortest to longest

• Calculate the perimeter of the triangle