Pythagorean Theorem Concepts

In lesson 12.2, the focus is on using the converse of the Pythagorean theorem to determine if a triangle is a right triangle based on its side lengths. The lesson includes three examples: triangles with sides 3, 4, 5; 7, 9, 12; and 6.1, 8.3, 10.9. Each example demonstrates the process of substituting the longest side for 'c' and checking if a^2 + b^2 equals c^2. The lesson concludes with a summary and an invitation for students to ask questions.

What is the main goal of using the converse of the Pythagorean theorem?

• To determine if a triangle is a right triangle

• To calculate the perimeter of a triangle

• To find the area of a triangle

• To find the angles of a triangle

In the first example, what are the side lengths of the triangle?

• 3, 4, 5

• 5, 12, 13

• 6, 8, 10

• 7, 24, 25

What is the result of applying the Pythagorean theorem to the triangle with sides 3, 4, and 5?

• The triangle is a right triangle

• The triangle is an isosceles triangle

• The triangle is an equilateral triangle

• The triangle is not a right triangle

In the second example, what is the longest side of the triangle?

• 10

• 12

• 9

• 7

What conclusion is reached for the triangle with sides 7, 9, and 12?

• It is an equilateral triangle

• It is not a right triangle

• It is an isosceles triangle

• It is a right triangle

What should be used as 'c' in the Pythagorean theorem?

• The longest side

• The shortest side

• Any side

• The side opposite the smallest angle

What is the significance of the triangle being inscribed in a circle in the final example?

• It guarantees the triangle is a right triangle

• It affects the calculation of side lengths

• It ensures the triangle is equilateral

• It means all vertices touch the circle

What are the side lengths of the triangle in the final example?

• 7.1, 9.3, 11.9

• 8.1, 10.3, 12.9

• 6.1, 8.3, 10.9

• 5.1, 7.3, 9.9

What is the result of the calculation for the triangle with sides 6.1, 8.3, and 10.9?

• The triangle is a right triangle

• The triangle is an equilateral triangle

• The triangle is not a right triangle

• The triangle is an isosceles triangle

What tool is suggested for calculating the squares of decimal numbers?

• A protractor

• A ruler

• A calculator

• A compass