Right Triangle Properties and Theorems

This lesson focuses on finding unknown side lengths in right triangles using equations. It covers identifying hypotenuses, solving for unknown sides, handling fractional side lengths, and working with composite figures. The lesson includes practical examples and homework problems to reinforce the concepts.

Which of the following equations is different from the others?

• a^2 = c^2 - b^2

• c^2 = a^2 - b^2

• b^2 = a^2 + c^2

• a^2 + b^2 = c^2

What is the hypotenuse in a right triangle?

• The side opposite the smallest angle

• The side opposite the right angle

• The longest side of any triangle

• The side adjacent to the right angle

When solving for a missing side in a right triangle, what should you ensure?

• The sides are labeled with numbers

• The hypotenuse is the shortest side

• The equation is set up with the hypotenuse as the longest side

• The triangle is equilateral

If a triangle has sides of 3, 4, and 5, which side is the hypotenuse?

• None of these

• 5

• 4

• 3

How do you find the missing side length in a right triangle with sides 2.4 and 6.5?

• Add the squares of the two sides

• Subtract the smaller side from the larger side

• Multiply the two sides

• Use the Pythagorean theorem

What is the result of taking the square root of 50?

• 25

• 7.07

• 10

• 5

In a right triangle with a side length of 1/4 and a hypotenuse of 1/3, what is the length of the other side?

• 1/12

• 1/8

• 1/9

• 1/16

What is the first step in solving a composite figure problem involving right triangles?

• Label all angles

• Identify the hypotenuse

• Find the area of the figure

• Calculate the perimeter

What is the purpose of the Pythagorean theorem in this lesson?

• To measure angles

• To find the area of a triangle

• To determine the type of triangle

• To calculate the length of a missing side

What is the expected weight of a newborn Doberman according to the lesson?

• 3 lbs

• 1.22 lbs

• 0 lbs

• 2.45 lbs