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Pythagorean Theorem

8.G.B.8
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Aligned To Common Core Standard:

Grade 8 Geometry - 8.G.B.8

When a triangle has a right side (measuring ninety degrees) and you extend each side with a square, the biggest square has the same exact are as the sum of the squares of the other two sides. If we labelled the longest side c and the other two sides (legs) a and b, we could sum up that phenomena with the equation a2 + b2 = c2. We term the longest side, that opposite the right angle, the hypotenuse. As you gather by the algebra, if you know the measures of any two sides of a right triangle, you can use this theorem to determine the third side. Pythagorean Theorem lends itself to all form of building and construction because it allows you to easily determine the length of any material that we using as long as you have two materials that meet at a right angle. Sailors use this all the time to find the shortest route between two points. You will find many applications in the field of surveying when cartographers and engineers are constructing maps that indicate steepness and slopes of areas.

Printable Worksheets And Lessons


  • Applying the Pythagorean Theorem Step-by-Step Lesson- The side that is missing is defined as the hypotenuse. We can tell this because it is directly opposite the right angle.
  • In Action Guided Lesson - Example: Given a right triangle with a hypotenuse of 27 and a leg of 17, what is the measure of the missing leg?
  • Guided Lesson Explanation - If this is a right triangle it will work out when the Pythagorean Theorem is applied to it. This means it will flow in the formula: leg2 + leg2 = hypotenuse2
  • Are They Right Triangles? - Determine the classification of these shapes.
  • Skills Review - We explore every way this topic can be looked at.




  • Review Sheets

    The coordinate graph makes it much more understandable than just labeling sides.

    • Review 1 - We will look this from the diagram perspective and in word form.
    • Review 2 - Another go at this series of skills.



    Homework Sheets

    The coordinate graph makes it much more understandable than just labeling sides.

    • Homework 1 - We will see if these shapes will work for us.
    • Homework 2 - Another approach at the first version.
    • Homework 3 - All of these shapes are much more narrow.
    • Homework 4 - You will find decimal lengths to work with.



    Practice Worksheets

    We start to find random distances between points.

    • Practice 1 - You will work with some really scaled down sides.
    • Practice 2 - We orientate these shapes from all directions.
    • Practice 3 - This is a basic look at this skill.
    • Practice 4 - More decimal lengths to work with.



    Math Skill Quizzes

    Here are more like problems to help you master this topic.

    • Quiz 1 - Use the Pythagorean theorem to find the length of the missing side of the right triangle.
    • Quiz 2 - Apply this formula to see if you can determine that missing side.
    • Quiz 3 - Time break out the decimal form one more time.