Pythagorean Theorem and Triangle Properties

This lesson covers finding side lengths of triangles, focusing on identifying unique triangle properties and using the Pythagorean Theorem. Students engage in activities to determine which triangle doesn't belong and complete tables for given triangles. The lesson introduces the Pythagorean Theorem, explaining its application in right triangles, and concludes with practice problems to reinforce understanding.

Which of the following triangles is an isosceles triangle?

• A triangle with all sides of different lengths

• A triangle with no equal sides

• A triangle with two sides of equal length

• A triangle with a 90° angle

What is the unique feature of triangle H in the 'Which One Doesn't Belong' activity?

• It has a side length of 5

• It has square roots in its side lengths

• It has a 90° angle

• It has two sides of the same length

In the table of triangles activity, what is the first step to find the side length of a triangle?

• Calculate the perimeter of the triangle

• Draw a circle around the triangle

• Draw a square around the triangle

• Measure the angles of the triangle

What is the area of a square with a side length of 2?

• 2

• 4

• 6

• 8

How do you calculate the side length of a square if you know its area?

• Add 2 to the area

• Take the square root of the area

• Divide the area by 2

• Multiply the area by 2

What is the Pythagorean theorem used for?

• Calculating the area of a circle

• Finding the side lengths of right triangles

• Determining the angles of a triangle

• Measuring the perimeter of a square

In a right triangle, what is the side opposite the right angle called?

• Leg

• Base

• Altitude

• Hypotenuse

Which of the following is true for a right triangle?

• All sides are of equal length

• It has no right angle

• The sum of the angles is 100°

• The sum of the squares of the legs equals the square of the hypotenuse

What is the formula for the Pythagorean theorem?

• a^2 + b = c^2

• a^2 = b^2 + c^2

• a + b = c

• a^2 + b^2 = c^2

What is the hypotenuse in a right triangle?

• The longest side

• The shortest side

• The side opposite the smallest angle

• The side adjacent to the right angle