Special Right Triangles and Their Properties

This lesson covers right triangles and the Pythagorean theorem, focusing on using the theorem to find missing sides. It also explores special right triangles, specifically 45-45-90 and 30-60-90 triangles, providing shortcuts for calculations. The lesson includes practical applications and emphasizes the importance of understanding these geometric concepts.

What is the main focus of Geometry Lesson 81?

• Proving the Pythagorean theorem

• Studying the history of geometry

• Learning about acute triangles

• Using the Pythagorean theorem and exploring special right triangles

In a right triangle, which side is the hypotenuse?

• The side opposite the smallest angle

• The side opposite the right angle

• The side that forms the right angle

• The longest side that forms the right angle

How can you verify if three given sides form a right triangle?

• Check if the sides are in arithmetic progression

• Ensure all angles are equal

• Use the formula a^2 + b^2 = c^2

• Check if the sum of the sides equals zero

What is a characteristic of a 45-45-90 triangle?

• It has two congruent sides and a hypotenuse that is the side length times the square root of 2

• It is an equilateral triangle

• It has two equal angles of 60 degrees

• It has one angle of 90 degrees and two angles of 30 degrees

In a 45-45-90 triangle, if one leg is 7, what is the hypotenuse?

• 14

• 7√2

• 7√3

• 7

What is the formula for the hypotenuse in a 30-60-90 triangle?

• Hypotenuse = 3 times the short side

• Hypotenuse = 2 times the short side

• Hypotenuse = short side times the square root of 3

• Hypotenuse = short side divided by 2

In a 30-60-90 triangle, if the short side is 5, what is the long side?

• 5

• 10

• 5√2

• 5√3

How do you rationalize a denominator with a square root?

• Multiply by the square root over itself

• Subtract the square root from the denominator

• Divide by the square root

• Add the square root to the numerator

What is the long side in a 30-60-90 triangle if the hypotenuse is 12?

• 6

• 6√3

• 12√3

• 12

What should you do if you have questions about the lesson?

• Search online for answers

• Wait until the next lesson

• Ignore them

• Ask the teacher for clarification