PYTHAGOREAN tHEOREM

Open Ended

How do you think the manufacturer got “50 inches” from a 40-by-30 box?

Open Ended

Which part of the box might actually measure 50 inches?

Open Ended

How can we check the accuracy of the label?

Open Ended

Can mathematics help explain this mystery?

Multiple Choice

Which side of a right-angled triangle is referred to as the hypotenuse?

• The longest side

• The shortest side

• Any side

• The side opposite the right angle

Open Ended

Based on the learning objectives, how can the Pythagorean Theorem be applied to solve real-life problems?

Open Ended

Why is it important to be able to classify triangles as right or not in everyday situations?

Multiple Select

Select all the properties that are true for a right triangle.

• It has one 90° angle

• The sum of its angles is 180°

• It has two equal sides

• The longest side is called the hypotenuse

Multiple Choice

Which of the following statements best describes a right triangle?

• A triangle with one 90° angle

• A triangle with all sides equal

• A triangle with no equal sides

• A triangle with all angles less than 90°

Multiple Select

Which of the following statements are true about the sides of a right triangle?

• The hypotenuse is always the longest side.

• The legs form the right angle.

• The legs are always equal in length.

• The hypotenuse is opposite the right angle.

Multiple Choice

Which side of a right triangle is opposite the right angle and is also the longest side?

• Hypotenuse

• Leg

• Base

• Altitude

Open Ended

Explain how the Pythagorean Theorem can be used to find the length of a missing side in a right triangle.

Multiple Choice

What is the name of the theorem that states the sum of the squares of the lengths of the legs of a right triangle equals the square of the length of the hypotenuse?

• Pythagorean Theorem

• Triangle Sum Theorem

• Sine Rule

• Cosine Rule

Multiple Choice

Given a right triangle with sides 8, 15, and 17, which side is the hypotenuse?

• 8

• 15

• 17

• Cannot be determined

Open Ended

Compare the process of identifying the hypotenuse in a triangle with numbers (like 8, 15, 17) versus with variables (like m, t, r). What is similar and what is different?

Multiple Select

Which of the following are always true about the legs of a right triangle?

• They are always equal in length.

• They form the right angle.

• They are shorter than the hypotenuse.

• They are always perpendicular to each other.

Open Ended

Explain how you can identify the hypotenuse in any right triangle.

Multiple Choice

Which side of a right triangle is always the longest?

• Leg

• Hypotenuse

• Base

• Altitude

Open Ended

What do you think could be inside the Mystery Box in Activity 1?

Open Ended

What is one thing you learned about math today that surprised you?