About Us

Why Choose StudyPug

How it works

Pricing

Testimonials

Contact Us

Blog

Basic Math

Algebra

Geometry

Trigonometry

Calculus

Linear Algebra

Differential Equations

Statistics

Chemistry

Organic Chemistry

Physics

Microeconomics

For Students

For Parents

For Home Schoolers

For Teachers

Australia

Canada

Ireland

New Zealand

Singapore

United Kingdom

United States

Sitemap

Terms of Service

Privacy Policy

Master the Pythagorean Theorem: Examples and Applications

EQAO Grade 9 Math: Master Core Concepts & Skills

Ratios, Rates, and Proportions

test

auto-gen

Ratios

Ratios - Find The Missing Value LHS

Ratios - Find The Missing Value RHS

Equivalent Ratios

Rates

Find the Biggest Rate 

Find the Unit Price 

Unit Rate Fill in Box

Find the Quickest Rate 

Unit Rate

Proportions

Proportions — Missing Denominator

Proportions — Missing Numerator

Proportions - Find the Missing Denominator LHS

Proportions - Find the Missing Denominator RHS

Proportions - Find the Missing Numerator LHS

Proportions - Find the Missing Numerator RHS

Square Roots

Squares and square roots

Square Root of a Perfect Square

Estimating square roots

Pythagorean Theorem

Introduction to pythagorean theorem

Using the pythagorean relationship

Applications of pythagorean theorem

Rational Numbers

Comparing and ordering rational numbers

Comparing decimal numbers

Comparing fractions

Solving problems with rational numbers in decimal form

Mixed Operations with Decimals

Mixed Operations

Mixed Operations with Decimals Bracket

Mixed Operations with Bracket Square

Solving problems with rational numbers in fraction form

Operations with fractions

Determine square roots of rational numbers

Square roots of rational numbers

Powers and Exponents

Using exponents to describe numbers

Expanded powers

Exponent rules

Single Power Expressions

Dividing powers

Multiplying powers

Order of operations with exponents

Using exponents to solve problems

Proportional Relationships

Understanding graphs of proportional relationships

Linear relations

Using tables of values to graph proportional relationships

Linear relation

Applications of proportional relationships

Identifying proportional relationships

Linear Ralations

Representing patterns in linear relations

Represent Patterns in Linear Relations Equation Decimal

Represent Patterns in Linear Relations Equation Integer Start From 0

Represent Patterns in Linear Relations Equation Integer Start From 1

Represent Patterns in Linear Relations Equation Negative Decimal

Identify the Linear Equation

Reading linear relation graphs

Solving linear equations by graphing

Solving Linear Equations

Solving linear equations using multiplication and division

Two-step Linear Equations LHS

Two-step Linear Equations RHS

Solving two-step linear equations: ax + b = c, x/a + b = c

Solving two-step linear equations: ax + b = c, x/a + b = c

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

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

Solving linear equations with variables on both sides

Introduction to Relations and Functions

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

Identifying functions

Function notation

Linear Functions

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

Midpoint formula: \(M = ( \frac{x_1+x_2}2  ,\frac{y_1+y_2}2)\)

Midpoint formula

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

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

General form: Ax + By + C = 0

Point-slope form: \(y - y_1 = m (x - x_1)\)

Graphing linear functions using table of values

Graphing linear functions using x- and y-intercepts

Graphing from slope-intercept form y=mx+b

Graphing linear functions using a single point and slope

Word problems of graphing linear functions

Rate of change

Parallel and perpendicular lines in linear functions

Applications of linear relations

Introduction to Polynomials

Characteristics of polynomials

What are polynomials

Equivalent expressions of polynomials

Adding and subtracting polynomials

Multiplication and Division of Polynomials

Multiplying and dividing monomials 

Divide a monomial by a monomial

Multiply a monomial by a monomial

Multiplying polynomials by monomials

Multiply a polynomial by a monomial

Dividing polynomials by monomials

Introduction to 3-Dimensional Objects

Introduction to surface area of 3-dimensional shapes

Nets of 3-dimensional shapes

Surface area of prisms

Surface Area of Prisms Rectangle

Calculate the Surface Area

Surface area of cylinders

Surface Area and Volume

Surface area and volume of prisms

Surface area and volume of pyramids

Surface area and volume of cylinders

Surface area and volume of cones

Surface area and volume of spheres

Circle Geometry

Angles in a circle

Chord properties 

Tangent properties

Data Management

Influencing factors in data collection

Classification of data

Characteristics of Quantitative Data

Classify the Level of Measurement

Identify the Level of Measurement

Sampling methods

Sampling Methods

Scatter plots and correlation

Census and bias

Census and Bias

Classifying Bias

Linear Programming

What is linear programming?

Finding Optimal Values Given Constraints In Slope-Intercept Form

Finding Optimal Values Given Constraints In Standard Form

Linear programming word problems

EQAO Grade 9 Principles of Math

sample

math

https://dmn92m25mtw4z.cloudfront.net/img/textbook/textbook-ca-eqao-9-principles-math.png

Intro

- 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.

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;. 

Pythagorean theorem

Examples of the pythagorean theorem

Introduction to Exponents

Classifying Triangles