Unlocking the Pythagorean Theorem: Finding Missing Sides

Math Grades 7th Grade 12:55 Video
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Lesson Description

Learn the basics of the Pythagorean Theorem and how to use it to find missing side lengths in right triangles. This lesson uses a video to explain the concepts and provide examples.

Video Resource

An Introduction to the Pythagorean Theorem | Math with Mr. J

Math with Mr. J

Duration: 12:55
Watch on YouTube

Key Concepts

  • Right Triangles
  • Hypotenuse
  • Legs of a Right Triangle
  • Pythagorean Theorem (a² + b² = c²)
  • Square Roots

Learning Objectives

  • Students will be able to identify the hypotenuse and legs of a right triangle.
  • Students will be able to apply the Pythagorean Theorem to find the missing side length of a right triangle given the other two side lengths.
  • Students will be able to explain the relationship between the sides of a right triangle as described by the Pythagorean Theorem.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the definition of a right triangle and its key components: the right angle, hypotenuse, and legs. Briefly discuss historical context of the Pythagorean Theorem.
  • Video Viewing (10 mins)
    Watch the 'An Introduction to the Pythagorean Theorem | Math with Mr. J' video. Encourage students to take notes on key terms and concepts as they watch.
  • Guided Practice (15 mins)
    Work through example problems together as a class. Start with simple examples where students identify the legs and hypotenuse, and then progress to solving for missing side lengths. Reiterate the importance of correctly identifying 'a', 'b', and 'c' in the formula a² + b² = c².
  • Independent Practice (15 mins)
    Assign practice problems for students to work on individually. Circulate to provide assistance and answer questions. Focus on problems that require students to find both the hypotenuse and a leg.
  • Wrap-up and Review (5 mins)
    Review the main concepts of the lesson and answer any remaining questions. Preview how the Pythagorean Theorem will be used in future lessons.

Interactive Exercises

  • Triangle Sort
    Provide students with a variety of triangle diagrams and have them sort the triangles into two groups: right triangles and non-right triangles. For the right triangles, have them label the hypotenuse and legs.
  • Missing Side Challenge
    Present students with a set of right triangles where one side length is missing. Have them use the Pythagorean Theorem to calculate the missing side length. Increase the difficulty by including problems with decimals or word problems.

Discussion Questions

  • Why is it important to correctly identify the hypotenuse in a right triangle?
  • Can the Pythagorean Theorem be used on any triangle? Why or why not?
  • Explain in your own words what the Pythagorean Theorem states.

Skills Developed

  • Problem-solving
  • Critical thinking
  • Application of formulas
  • Algebraic manipulation

Multiple Choice Questions

Question 1:

Which side of a right triangle is always opposite the right angle?

Correct Answer: Hypotenuse

Question 2:

The Pythagorean Theorem applies to what type of triangles?

Correct Answer: Right triangles

Question 3:

In the Pythagorean Theorem, a² + b² = c², which side does 'c' represent?

Correct Answer: The hypotenuse

Question 4:

If a = 3 and b = 4, what is the value of c in a right triangle?

Correct Answer: 5

Question 5:

What is the first step in solving for a missing leg in a right triangle using the Pythagorean Theorem?

Correct Answer: Subtract the square of the hypotenuse from the square of the other leg

Question 6:

If the hypotenuse of a right triangle is 13 and one leg is 5, what is the length of the other leg?

Correct Answer: 12

Question 7:

The legs of a right triangle are the ______ sides to the right angle.

Correct Answer: Adjacent

Question 8:

Why is it crucial to correctly identify the hypotenuse when using the Pythagorean Theorem?

Correct Answer: All of the above

Question 9:

What mathematical operation is used to isolate the variable when finding the length of a side?

Correct Answer: Square Root

Question 10:

A visual representation of the Pythagorean Theorem can be shown by creating _______ on each side of the right triangle

Correct Answer: Square

Fill in the Blank Questions

Question 1:

The side opposite the right angle in a right triangle is called the ________.

Correct Answer: hypotenuse

Question 2:

The Pythagorean Theorem is expressed as the equation a² + b² = ________.

Correct Answer: c²

Question 3:

The two shorter sides of a right triangle are called ________.

Correct Answer: legs

Question 4:

If a = 6 and b = 8, then c = ________.

Correct Answer: 10

Question 5:

To find the value of 'a' when given 'b' and 'c', you must ________ the square of 'b' from the square of 'c'.

Correct Answer: subtract

Question 6:

A triangle with one angle measuring 90 degrees is a _________ triangle.

Correct Answer: right

Question 7:

When you square root 64 you get _______.

Correct Answer: 8

Question 8:

The Pythagorean Theorem equation is _____ + _____ = c².

Correct Answer: a² / b²

Question 9:

A _____ on each side of a right triangle can visually represent the Pythagorean Theorem.

Correct Answer: square

Question 10:

The relationship between the sides of a _____ triangle are represented in the Pythagorean Theorem.

Correct Answer: right

Educational Standards

CCSS.Math.Content.7.G.B.6:Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. CCSS.Math.Content.8.G.B.7:Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. CCSS.Math.Content.8.EE.A.2:Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

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