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Similar Polygons: Definition, Examples, and Applications

Demonstrate understanding of income and calculate gross and net pay

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Taxes, discounts, tips and more

Discounts — Word Problem

Taxes — Word Problem

Percentage - Applying a Discount Price– Word Problem

Percentage - Applying a Discount Percent – Word Problem

Percentage - Applying a Tax Total – Word Problem

Percentage - Applying a tax Percent – Word Problem

Simple interest

Simple Interest — Word Problem

Basic Concepts of Simple Interest – Word Problem

Borrowing Money for More Than One Year  – Word Problem

Investigate the Advantages of Borrowing Money  – Word Problem

Solve problems involving compound interest in financial decision making

Finance: Compound interest

Finance: Compound Interest

Finance: Future value and present value

Analyse costs and benefits of renting, leasing and buying

Demand, revenue, cost & profit

Marginal revenue, and maximizing revenue & average revenue

Marginal cost, and minimizing cost & average cost

Develop a budget for a given set of circumstances

Marginal profit, and maximizing profit & average profit

Elasticity of demand

Consumer and producer surplus

Demonstrate understanding of basic geometric concepts

Angle in standard position

Coterminal angles

Coterminal Angles

Classifying triangles

Isosceles and equilateral triangles

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

Demonstrate understanding of parallel and perpendicular lines

Parallel line equation

Perpendicular line equation

Combination of both parallel and perpendicular line equations

Parallel and perpendicular lines in linear functions

Applications of linear relations

Demonstrate understanding of triangles

Similar triangles

Similar polygons

Law of sines

Ambiguous case: SSA triangles

Law of cosines

Analyse and prove conjectures using inductive reasoning to solve problems

Rolle's Theorem

Arithmetic sequences

Geometric sequences

Mean value theorem

Mean Value Theorem

Mean Value Theorem Application

Demonstrate understanding of logical reasoning

Absolute value functions

Expressing an Absolute Value Linear Function as a Piecewise Function

Expressing an Absolute Value Quadratic Function as a Piecewise Function

Null hypothesis and alternative hypothesis

Proving claims

Confidence levels, significance levels and critical values

Analyse and prove conjectures using deductive reasoning to solve problems

Factor by taking out the greatest common factor

Factor by taking out GCF

Factor by grouping

Test statistics

Traditional hypothesis testing

Traditional Mean Hypothesis Testing

P-value hypothesis testing

Proportion Hypothesis Testing

Use logical reasoning to write geometric and algebraic proofs

Factoring difference of squares: \(x^2 - y^2\)

Factoring difference of squares: <katex>x^2 - y^2</katex>

Factoring difference of squares: x^2 - y^2

Factoring trinomials

Factoring Trinomials

Analyse and prove conjectures using indirect proof

Mean hypothesis testing with t-distribution

Hypothesis Testing Mean Claims without Knowing <katex> \sigma </katex>

Type 1 and type 2 errors

Type 1 and Type 2 Errors

Demonstrate understanding of the probability of an event

Fundamental counting principle

Fundamental Counting Principle Involving Restrictions

Permutations

Combinations

Addition rule for 

Addition Rule for "OR"

Addition rule for "OR"

Multiplication rule for 

Multiplication rule for "AND"

Multiplication Rule for "AND"

Interpret and assess the validity of odds and probability statements

Conditional probability

Probability involving permutations and combinations

Demonstrate understanding of events that are independent or dependent

Probability of independent events

Law of total probability

Law of Total Probability

Probability of a randomly selected employee meeting a sales target

Probability of a randomly selected driver being involved in an accident

Probability of a randomly selected customer making a purchase

Probability of a randomly selected person being overweight

Bayes' rule

Bayes" Rule

Bayes rule

Bayes" rule

Bayes' Rule

Probability with Venn diagrams

Demonstrate understanding of events that are mutually exclusive and not mutually exclusive

Probability distribution - histogram, mean, variance & standard deviation

Binomial distribution

Binomial Distribution

Mean and standard deviation of binomial distribution

Interpreting Mean and Standard Deviation of Binomial

Demonstrate understanding of data and statistics

Classification of data

Characteristics of Quantitative Data

Classify the Level of Measurement

Identify the Level of Measurement

Sampling methods

Sampling Methods

Census and bias

Census and Bias

Classifying Bias

Represent data visually in various ways

Frequency distribution and histograms

Stem and leaf plots

The Leaf and Stem of Numbers

Recognizing the Leaf and Stem of Numbers

Recognizing The Leaf And Stem of Numbers Leaf

Recognizing The Leaf And Stem of Numbers Stem

Reading Stem and Leaf Plots — Median

Reading Stem and Leaf Plots — Range

stem and leaf plots Range

Reading Stem and Leaf Plots

Reading Stem and Leaf Plots — Mean

Reading Stem and Leaf Plots — Mode

Frequency polygons

Shapes of distributions

Demonstrate understanding of measures of central tendency

Center of a data set: mean, median, mode

Demonstrate understanding of measures of dispersion

Spread of a data set - standard deviation & variance

Measures of relative standing - z-score, quartiles, percentiles

Demonstrate understanding of correlation and regression

Bivariate, scatter plots and correlation

Regression analysis

Equation of the best fit line

Demonstrate understanding of the normal distribution

Introduction to normal distribution

The Normal Distribution and the 68-95-99.7 Rule

Using "invNorm" to Solve Normal Distribution Problems

Normal distribution and continuous random variable

Z-scores and random continuous variables

Pre-Calculus Elective 11 (MAT521E)

Financial Mathematics

Logical Reasoning

Probability

math

Intro

<p>- Hi. Welcome to this question right here. So we're here to find the perimeter, which is all the sides added up together, of the smaller quadrilateral right here. Okay? So it seems like we&apos;ve got a big one and a small one. Now, I guess it's by assuming they are similar to each other, or else we cannot do this question. So we know the big quadrilateral on the outside is 25.2, 21, 44.1, 33.6. We're looking for this number, this number and that number right there in order to calculate the total perimeter, right? So far we're given. . .the information we have is the 25.2 and the 16.8 here. They are the similar sides of the two figures, right? So figuring out the ratio is the first thing you have to do. So the ratio is take the bigger one, 25.2, divided by the smaller one, 16.8, and let's see what we&apos;ve got. 25.2 divided by 16.8, we have a 1.5, which is a good number. I like that. Okay? So the ratio is one and a half. So it means the bigger one is one and a half times bigger than the smaller one. So how do we figure out the rest of the information? We're just going to do it one at a time. So what happens is this is the big one, right? That is the smaller one. So you can actually just say that 33.6 divided by the smaller one is equal to 1.5. Okay?<br />
For this missing side right there. So all we have to do is just crisscross these two guys. So mathematically to figure out the answer is actually just 33.6 divided by 1.5. So let me work that out for you right here. So 33.6 divided by 1.5 will give you this missing box, which is 33.5 divided by 1.5. We have 22.33. Okay? 22.33 repeating. So what happens is we're going to go ahead and do the same thing to every single side. Okay? So for the next one right there, we're going to follow the same math. 44.1 divided by 1.5. Okay. Sorry about my writing right there. Let's put 1.5 one more time. So 44.1 divided by 1.5, we&apos;ve got ourselves 29.4. So this is my 29.4 right there. Okay? So I'm going to write down 29.4 on this side. And finally you come down to the last one, the last person right there. It's the 21 divided by 1.5 again. So we&apos;ve got 21 divided by 1.5. It's just 14. How nice. We&apos;ve got a nice number finally. So this one here turns out to be a 14. So to get the total perimeter, guess what? It's just the 16.8, plus the 22.33, plus the 29.4 and finally the 14 at the very last. Okay?<br />
So 16.8 plus the 22.333 plus the 29.4 and the 14 at the very end. We&apos;ve got ourselves 82.53. Okay? 82.53. And that is your final answer. If you add up all of the sides of the smaller quadrilateral, that is the perimeter. Thanks for watching.</p>


In this lesson, we will learn how to determine whether a pair of polygons is similar to each other. Once we know that the polygons are similar, we can calculate unknowns such as, side lengths, scale factors, and surface areas.

Understanding similar polygons

Enlargements and reductions with scale factors

Scale diagrams