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Master the Pythagorean Theorem: Examples and Applications

8.EE.A.1

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Using exponents to describe numbers

Expanded powers

Exponent rules

Single Power Expressions

Dividing powers

Multiplying powers

Order of operations with exponents

Product rule of exponents

Quotient rule of exponents

Power of a product rule

Power of a quotient rule

Power of a power rule

Simplify the power

8.EE.A.2

Squares and square roots

Square Root of a Perfect Square

Square and square roots

Cubic and cube roots

Cube root of a perfect cube

Converting radicals to mixed radicals

Converting radicals to entire radicals

8.EE.A.3

Scientific notation

8.EE.B.5

Parallel and perpendicular lines in linear functions

Understanding graphs of linear relationships

Linear relations

Understanding tables of values of linear relationships

Linear relation

Applications of linear relationships

Identifying proportional relationships

8.EE.B.6

Slope equation: \(m = \frac{y_2-y_1}{x_2- x_1}\)

Slope equation: <katex>m = \frac{y_2-y_1}{x_2- x_1}</katex>

Slope intercept form:  y = mx + b

Slope intercept form: y = mx + b

8.EE.C.7

Introduction to linear equations

Model and solve one-step linear equations: ax = b, x/a = b

One-step Linear Equations

One Step Linear Equations — Word Problem

One-step equations

One-step Equations LHS

One-step Equations RHS

Model And Solve One Step Linear Equations Divide – Word Problem

Model And Solve One Step Linear Equations Multiply – Word Problem

Solving two-step linear equations using addition and subtraction: ax + b = c

Two-step Linear Equations

Two-step Linear Equations LHS

Solve Linear Equations Using Addition and Subtraction – Word Problem

Two-step Linear Equations — Word Problem

Solving two-step linear equations using multiplication and division: x/a + b = c

Two-step Linear Equations RHS

Solving two-step linear equations using distributive property: a(x + b) = c

Solve Linear Equations Using Distributive Property – Word Problem

Solving literal equations

8.EE.C.8

Determining number of solutions to linear equations

Solving systems of linear equations by graphing

Solving systems of linear equations by elimination

Solving systems of linear equations by substitution

8.F.A.1

Relationship between two variables

Identifying functions

8.F.A.2

Function notation

8.F.B.4

Applications of linear relations

8.F.B.5

Graphing linear functions using table of values

8.G.A.1

Line symmetry

Tessellations using translations and reflections

tessellations using translations and reflections

8.G.A.2

Rotational symmetry and transformations

8.G.A.3

Enlargements and reductions with scale factors

Tessellations using rotations

8.G.A.4

Similar polygons

8.G.A.5

Similar triangles

8.G.B.6

Pythagorean theorem

Pythagorean Theorem

8.G.B.7

Using the pythagorean relationship

8.G.B.8

Distance formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Distance formula: <katex>d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}</katex>

Distance formula

Applications of pythagorean theorem

8.G.C.9

Volume of cylinders

Word problems relating volume of prisms and cylinders

Surface area and volume of cones

Surface area and volume of spheres

8.NS.A.1

Understanding the number systems

Rational vs. Irrational numbers

8.NS.A.2

Determine square roots of rational numbers

Square roots of rational numbers

Estimating square roots

Converting repeating decimals to fractions

8.SP.A.1

Reading linear relation graphs

Box-and-whisker plots and scatter plots

8.SP.A.2

Solving linear equations by graphing

8th Grade Math

math

Intro

<p>- Hi and welcome to this question right here. We're trying to find the side lengths of the squares. So as you can see we&apos;ve got 1, 2, 3 different squares right here and with a right triangle in the middle. This square here we already know all the sides. It's 18, 18, 18, 18. Where as this one here is 24, 24, 24, 24. Now we're probably trying to figure out this one over here. If you can figure out this one then that means you figured out all the side length of this big rectangle...sorry, square. The only hint that we have is that this is a 90 degrees. So if you have a 90 degrees that means you can go ahead and use a Pythagoras which is C squared equals A squared plus the B squared and that's the formula you want to memorize. So what happened is the C is always the hypotenuse, the longest side of the right triangle. So we're going to call this one C right here. We don't know what the C is. We're going to square the whole thing to solve for C. Remember you had to square root both sides so they can solve the C. For A and B it's your choice. You can choose whatever you like. You get the 18 and 24. So A and B are just two lengths of that right triangle. So you can punch in 18 for the A and the 24 for the B. So what happens at the end, you go 18 square. We have 324 for this number and 24 squared for 576. And you square root the whole thing. Make sure you add them before you square, though. 324 plus 576. I got a 900. So to show you all the work. So square root of that we&apos;ve got ourselves just 30, okay? So that means this C over here, this hypotenuse of this triangle, is going to be a 30 centimeter and that is the side of this square over here and that's what they're looking for. So your answer is just 30 centimeter. Thanks for watching.</p>

In the nutshell, Pythagorean theorem/Pythagorean relationship describes the relationship between the lengths and sides of a right triangle. After thousands of repeated examinations by the ancient Greek mathematicians, it was found that the square of the hypotenuse is equal to the sum of the squares of the other two sides c&sup2; = a&sup2; + b&sup2;. 

Introduction to pythagorean theorem

Examples of the pythagorean theorem

Introduction to Exponents

Classifying Triangles