Triangle Properties and Theorems

The video tutorial covers the Pythagorean Theorem and its converse, explaining how to find missing side lengths in right triangles and determine triangle types. It includes examples of Pythagorean triples and advanced algebraic problems. The converse is used to classify triangles as right, acute, or obtuse. The tutorial concludes with an application of the theorem in solving rectangle problems.

What is the primary use of the Pythagorean Theorem?

• To determine the type of triangle

• To find the area of a triangle

• To calculate the perimeter of a triangle

• To find missing side lengths of right triangles

Which statement correctly represents the Pythagorean Theorem?

• If a triangle is obtuse, then a^2 + b^2 = c^2

• If a triangle is equilateral, then a^2 + b^2 = c^2

• If a triangle is acute, then a^2 + b^2 = c^2

• If a triangle is right, then a^2 + b^2 = c^2

In a right triangle, what is the side opposite the right angle called?

• Hypotenuse

• Height

• Base

• Leg

Which of the following is a Pythagorean triple?

• 2, 3, 4

• 7, 24, 25

• 8, 15, 18

• 5, 12, 13

What is the unknown side length in a triangle with legs 40 and x, and hypotenuse 85?

• 75

• 95

• 65

• 85

Which of the following is NOT a Pythagorean triple?

• 10, 24, 26

• 3, 4, 5

• 6, 8, 10

• 9, 12, 15

What is the value of x if x^2 + 2x + 1 + x^2 + 6x + 9 = x^2 + 15x?

• 2

• 3

• 4

• 5

What is the converse of the Pythagorean Theorem?

• If a^2 + b^2 > c^2, then the triangle is obtuse

• If a^2 + b^2 < c^2, then the triangle is acute

• If a^2 + b^2 = c^2, then the triangle is equilateral

• If a^2 + b^2 = c^2, then the triangle is right

If a^2 + b^2 is greater than c^2, what type of triangle is it?

• Right

• Acute

• Obtuse

• Scalene

Which condition must be met for three side lengths to form a triangle?

• The sum of any two sides must be equal to the third side

• The sum of all sides must be equal

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

• The sum of any two sides must be greater than the third side