Exploring the Pythagorean Theorem and Special Right Triangles

This video tutorial explores Pythagoras theorem and its relation to triangle similarity, leading into trigonometry. It covers constructing and analyzing similar triangles, applying Pythagoras theorem to solve for side lengths, and comparing triangles using algebra. The video also introduces Pythagorean triples and special right triangles, such as isosceles and 30-60-90 triangles, providing a comprehensive understanding of these geometric concepts.

What theorem is used to relate the sides of a right triangle?

• Fermat's Last Theorem

• Euclid's theorem

• Thales' theorem

• Pythagoras theorem

How many similar triangles are formed when an altitude is drawn in a right triangle?

• Three

• Four

• Two

• One

What property is used to find the legs of a right triangle using Pythagoras theorem?

• Sum of angles in a triangle

• Angle-Side-Angle similarity

• The square of the hypotenuse

• The square of the legs

How can you verify a triangle is right using Pythagoras theorem?

• Sum of angles equals 180 degrees

• It has one 90 degree angle

• The square of the hypotenuse equals the sum of the squares of the other two sides

• All sides are equal

What makes Pythagorean triples special?

• They form equilateral triangles

• They only exist in theoretical mathematics

• Their sides form an arithmetic sequence

• Their sides are all integers

Which of the following is a Pythagorean triple?

• 3-4-5

• 2-3-4

• 5-6-7

• 6-8-9

What is the ratio of sides in an isosceles right triangle?

• 1:1:√2

• 1:√2:2

• 1:2:√3

• 1:√3:2

What is the hypotenuse of an isosceles right triangle if one leg is 5?

• 7.5

• 5√3

• 10

• 5√2

In a 30-60-90 triangle, if the shorter leg is 2, what is the length of the hypotenuse?

• 3

• 2√3

• 4

• 2√2

What is the process called when eliminating a radical from the denominator?

• Simplifying

• Factoring

• Rationalizing the denominator

• Expanding