Understanding the Pythagorean Theorem

Mr. Holcomb revisits the Pythagorean theorem in lesson 15, starting with a right triangle ABC. He draws an altitude to create three similar triangles and uses these to prove the theorem: a² + b² = c². The lesson concludes with a geometric exploration of the theorem's consequences, demonstrating how the areas of squares on the triangle's sides relate to the theorem.

What is the primary goal of the lesson involving triangle ABC?

• To calculate the area of triangle ABC

• To find the perimeter of triangle ABC

• To prove the Pythagorean Theorem

• To determine the angles of triangle ABC

What geometric construction is used to create three similar triangles?

• Drawing a median

• Drawing an altitude

• Drawing a tangent

• Drawing a bisector

How are the three triangles proven to be similar?

• By using side-angle-side similarity

• By using side-side-side similarity

• By using angle-side-angle similarity

• By using angle-angle similarity

What are the segments on the hypotenuse labeled as?

• x and z

• y and z

• x and y

• a and b

What is the expression for segment x in terms of b and c?

• x = a^2 / c

• x = b^2 / a

• x = c^2 / b

• x = b^2 / c

What equation is used to prove the Pythagorean Theorem algebraically?

• x + y = a + b

• x + y = a

• x + y = b

• x + y = c

What is the geometric consequence explored in the lesson?

• The relationship between areas of squares

• The relationship between perimeters

• The relationship between angles

• The relationship between volumes

How is the area of the square on side b related to the triangles?

• It is equal to the area of rectangle 1

• It is equal to the area of rectangle 2

• It is equal to the area of the original triangle

• It is equal to the area of the square on side a

What does the sum of the areas of the two smaller squares equal?

• The area of the square on the hypotenuse

• The area of the original triangle

• The area of the rectangle

• The area of the circle

What is the final conclusion of the lesson?

• a^2 + b^2 = c^2

• a^2 + b^2 = a^2

• b^2 + c^2 = a^2

• a^2 + c^2 = b^2