Right Triangle Properties and Applications

This lesson covers the converse of the Pythagorean theorem, using a clock hands activity to explore triangle properties. It explains how to determine if a triangle is a right triangle by checking if the side lengths satisfy the theorem. The lesson includes examples and calculations of unknown leg lengths in right triangles, followed by homework problems to reinforce the concepts.

What is the maximum distance between the tips of the clock hands if the hour hand is 3 cm and the minute hand is 4 cm?

• 6 cm

• 8 cm

• 5 cm

• 7 cm

Which of the following is a correct application of the Pythagorean Theorem?

• a^2 + b^2 = c^2

• a^2 = b^2 + c^2

• a^2 + b^2 = c

• a + b = c^2

If a triangle has sides 3, 4, and 5, what type of triangle is it?

• Equilateral

• Isosceles

• Right

• Scalene

How do you find the unknown side of a right triangle if you know the other two sides?

• Divide the known sides

• Multiply the known sides

• Subtract the squares of the known sides

• Add the squares of the known sides

What is the approximate value of the square root of 45?

• 6.9

• 6.7

• 6.5

• 7.1

Which of the following changes can make a non-right triangle into a right triangle?

• Decrease the shortest side

• Increase the shortest side

• Decrease the longest side

• Increase the longest side

If a right triangle has a hypotenuse of 15, which of the following could be the lengths of the other two sides?

• 7 and 10

• 9 and 12

• 5 and 12

• 8 and 11

In the homework problem, what is the initial amount of dollars Andre exchanges for pesos?

• $600

• $500

• $400

• $300

What is the result of 10 squared plus 10.5 squared?

• 230.25

• 220.25

• 210.25

• 200.25

Which of the following triangles does not satisfy the Pythagorean Theorem?

• 9, 12, 15

• 5, 12, 13

• 7, 24, 25

• 8, 15, 17