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Master SAS Similarity Theorem: Prove Triangle Similarity

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

- Hi, welcome to this question right here. So, we have two similar triangles right here. That did tell us it's similar, right? So, don't worry about it. It is similar. We need to calculate the missing length. Turns out the missing length is right here, okay? 
So, what you do first is you have to set up like a proportional fraction. So, let's put an equal sign right here. And put up a fraction sign and a fraction sign. So, what you do is this, you know that these two are similar triangles, okay? So, the shorter side with the shorter side, there's a ratio that's involved between these two so, my own little preference is I'm gonna take the bigger number that goes first. So, I'm gonna put a two right here, for the bigger triangle. This side right here versus this side, which is 0.5, okay? 
Then, I'm gonna try to figure out my missing x right here. So, this missing x corresponds to the six over here, okay? 
Because the hypotenuse and the hypotenuse of the two triangles would go together. So, the six over here of my bigger triangle will match the x here for my little triangle. So once again, the bigger on the top, smaller on the bottom. Just because the math is easier. The six is over here, and the x is over here, okay? 
Now, maybe now you're not go with the algebra. But you can just think about this. They are the same ratio to each other. All you need to do is think about how to go from two to six. Well, mathematically, going from two to six, you just have to times it by three. And since you times by three to the top, you have to do the same thing to the bottom, right? 
So, 0.5 times by 3, you get yourself a 1.5 at the very end. So, x over here turns out just to be a 1.5 meters. And that is your final answer. Thanks for watching.

Learn how to determine similar triangles by using side-side-side (SSS) similarity, <a href='[[glossary.html|{"keyword":"SAS Similarity"}]]'>side-angle-side (SAS) similarity</a> and the properties of similar triangles to solve questions. It's always a good idea to refresh your memory on scale factors and proportions because we will be using them a lot in this lesson.

Identifying similar triangles

Enlargements and reductions with scale factors

Ratios