Right Triangle Concepts and Properties

This lesson introduces Module S, focusing on irrational numbers and the Pythagorean theorem. It begins with a review of the theorem and its application to various triangles, including exercises to find missing sides and verify right triangles. The lesson progresses to solving example problems, including an advanced example involving an equilateral triangle. Students are guided through exercises to estimate side lengths using perfect squares. The lesson concludes with a summary and preparation for the next lesson on square roots.

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

• Geometric shapes

• Irrational numbers

• Rational numbers

• Algebraic expressions

In a right triangle, if one leg is 15 cm and the hypotenuse is 17 cm, what is the length of the other leg?

• 10 cm

• 8 cm

• 9 cm

• 7 cm

How can you determine if a triangle is a right triangle using the Pythagorean theorem?

• Check if all angles are equal

• Check if the sum of the squares of two sides equals the square of the third side

• Check if the triangle is isosceles

• Check if the triangle is equilateral

If c^2 = 97, which two perfect squares is 97 between?

• 81 and 100

• 100 and 121

• 49 and 64

• 64 and 81

What is the approximate length of a side if c^2 = 97?

• 9.5 cm

• 9.85 cm

• 10.5 cm

• 10 cm

In an equilateral triangle with a height of 10 cm, what is the approximate length of each side?

• 13 cm

• 10 cm

• 12 cm

• 11 cm

What is the significance of the hypotenuse in a right triangle?

• It is the shortest side

• It is the longest side

• It is equal to one of the legs

• It is always 10 cm

How do you find the missing side length in a right triangle if the square of the length is not a perfect square?

• Use a calculator to find the exact value

• Use the length of the hypotenuse

• Estimate using the nearest perfect squares

• Assume it is a perfect square

What is a perfect square?

• A number that is always even

• A number that is the product of two different integers

• A number that is the product of an integer multiplied by itself

• A number that is always odd

When estimating the length of a side in a right triangle, why is it important to know the nearest perfect squares?

• To provide a reasonable estimate

• To determine if the triangle is equilateral

• To find the exact length

• To check if the triangle is isosceles