Properties of Special Right Triangles

This video tutorial covers methods to find missing side lengths and angles in right triangles, focusing on the Pythagorean theorem and special right triangles (45-45-90 and 30-60-90). It provides detailed explanations and examples, demonstrating how to apply these concepts to solve problems. The tutorial also discusses the converse of the Pythagorean theorem and the importance of maintaining exact values in radical form.

What is the primary focus of the first lesson in this chapter?

• Trigonometry

• Geometry of Circles

• Pythagorean Theorem and Special Right Triangles

• Algebraic Equations

Which theorem is used to find the third side of a right triangle when two sides are known?

• Tangent Rule

• Pythagorean Theorem

• Cosine Rule

• Sine Rule

What does the converse of the Pythagorean theorem help determine?

• If a triangle is isosceles

• If a triangle is scalene

• If a triangle is equilateral

• If a triangle is a right triangle

In a 45-45-90 triangle, what is the relationship between the legs?

• One leg is half the hypotenuse

• Both legs are equal

• One leg is twice the other

• Legs are unrelated

How do you find the hypotenuse in a 45-45-90 triangle?

• Multiply one leg by √2

• Multiply one leg by √3

• Add the lengths of the legs

• Divide one leg by 2

If the hypotenuse of a 45-45-90 triangle is 6√2, what is the length of each leg?

• 6

• 3

• 6√2

• 3√2

In a 30-60-90 triangle, how is the hypotenuse related to the shorter leg?

• It is equal to the shorter leg

• It is twice the shorter leg

• It is half the shorter leg

• It is three times the shorter leg

What is the relationship between the longer leg and the shorter leg in a 30-60-90 triangle?

• Longer leg is half the shorter leg

• Longer leg is twice the shorter leg

• Longer leg is equal to the shorter leg

• Longer leg is √3 times the shorter leg

If the shorter leg of a 30-60-90 triangle is 5, what is the length of the hypotenuse?

• 10

• 5√3

• 5

• 15

In a 30-60-90 triangle, if the longer leg is 9, what is the length of the shorter leg?

• 6

• 3

• 3√3

• 9