Exploring 45-45-90 Triangles and the Pythagorean Theorem

The video tutorial covers the Pythagorean theorem, providing practice problems to solve for the hypotenuse and other sides of right triangles. It introduces the concept of identifying the hypotenuse and solving for unknown sides. The tutorial also explores the properties of a 45-45-90 triangle, explaining how to use angle information to determine side lengths. The video emphasizes understanding and applying the theorem in various scenarios.

What is the length of the hypotenuse when the sides of the right triangle are 6 and 7?

• Square root of 85

• Square root of 100

• Square root of 77

• Square root of 50

Which of the following is a correct representation of the Pythagorean theorem?

• a^2 + c^2 = b^2

• b^2 = a^2 + c^2

• a^2 = b^2 + c^2

• a^2 + b^2 = c^2

How can the square root of 85 be estimated between two integers?

• Between 7 and 8

• Between 10 and 11

• Between 8 and 9

• Between 9 and 10

What is the value of the unknown side 'A' when the hypotenuse is 10 and another side is 3?

• Square root of 91

• Square root of 81

• Square root of 85

• Square root of 100

Is 91 a prime number?

• Cannot be determined

• Yes

• No

• Irrelevant to the problem

What theorem is used to determine that the non-shared sides in a triangle with two equal angles are also equal?

• Right Triangle Theorem

• Isosceles Triangle Theorem

• Equilateral Triangle Theorem

• Scalene Triangle Theorem

What is the relationship between the angles and sides in a triangle with two angles of 45 degrees each?

• No specific relationship

• Only the hypotenuse is equal to the sum of the sides

• The sides opposite these angles are unequal

• The sides opposite these angles are equal

In a 45-45-90 triangle, if one side is 5, what is the length of the hypotenuse?

• 7.5

• 5

• 10

• 5 square roots of 2

What is the correct formula to calculate the length of the hypotenuse in a right triangle?

• side1 + side2

• side1^2 + side2^2

• Square root of (side1^2 - side2^2)

• Square root of (side1^2 + side2^2)

Which of the following is not a correct step in applying the Pythagorean theorem?

• Subtract the squares of the two shorter sides from the square of the hypotenuse

• Take the square root of the sum of the squares of the two shorter sides

• Add the squares of the two shorter sides to find the square of the hypotenuse

• Identify the longest side as the hypotenuse