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 SAS Similarity Theorem: Prove Triangle Similarity

Describe linear relations through patterns, graphs, tables, equations, interpolation and extrapolation

auto-gen

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

Identifying 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

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

General form:  Ax  + By  + C = 0

General form: Ax + By + C = 0

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

Graphing from slope-intercept form y=mx+b

Graphing linear functions using a single point and slope

Word problems of graphing linear functions

Function notation

Rate of change

Parallel and perpendicular lines in linear functions

Applications of linear relations

Solve problems using sine law and cosine law, excluding ambiguous case

Law of sines

Ambiguous case: SSA triangles

Law of cosines

Applications of the sine law and cosine law

Solve problems involving triangles, quadrilaterals, and regular polygons

Similar triangles

Similar polygons

Isosceles and equilateral triangles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

Demonstrate understanding of 2-D and 3-D transformations

Combining transformations of functions

Line symmetry

Rotational symmetry and transformations

Enlargements and reductions with scale factors

Scale diagrams

Transformations of functions: Horizontal translations

Transformations of functions: Vertical translations

Reflection across the y-axis: y = f(-x)

Reflection across the x-axis: y = -f(x)

Transformations of functions: Horizontal stretches

Transformations of functions: Vertical stretches

Demonstrate understanding of measuring instrument limitations and solve problems

Upper and lower bound

Upper and Lower Bound

Conversions between metric and imperial systems

Metric to Imperial Conversions

Imperial to Metric Conversions

Conversions Between Metric and Imperial Systems Speed KM to MI

Conversions Between Metric and Imperial Systems Speed  MI to M

Metric-Imperial Length Conversion Inch To Cm

Metric-Imperial Length Conversion MM/CM/M/KM To FT

Metric-Imperial Length Conversion MM/CM/M/KM To MI

Metric systems

Add and Subtract Mixed Units

Metric Length Conversion

Add or Subtract Different Metric Units Convert to CM

Add or Subtract Different Metric Units Convert to M

Add or Subtract Different Metric Units Convert to MM

Imperial systems

Imperial Length Conversion

Conversions involving squares and cubic

Imperial to Metric Conversions — Squares and Cubes

Imperial Conversion — Squares and Cubes

Metric to Imperial Conversion — Squares and Cubes

Metric Area Conversion FT to CM

Metric Area Conversion Foot to Inch

Metric Area Conversion M/CM to Inch

Analyze puzzles and games involving logical reasoning using problem-solving techniques

Direct variation

Identifying direct variations

Evaluating piecewise functions

Graphing piecewise linear functions

Graphing piecewise non-linear functions

Solve problems involving vehicle acquisition by buying, leasing, or leasing to buy

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

Finance: Future value and present value

Critique small business options considering expenses, sales, profit or loss

Marginal profit, and maximizing profit & average profit

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

Inverse variation

Joint and combined variation

Finance: Compound interest

Finance: Compound Interest

Continuous growth and decay

Demand, revenue, cost & profit

Marginal revenue, and maximizing revenue & average revenue

Marginal cost, and minimizing cost & average cost

Analyze and interpret problems involving probability

Addition rule for 

Addition Rule for "OR"

Addition rule for "OR"

Multiplication rule for 

Multiplication rule for "AND"

Multiplication Rule for "AND"

Conditional probability

Probability involving permutations and combinations

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

Solve problems involving measures of central tendency

Frequency distribution and histograms

Center of a data set: mean, median, mode

Spread of a data set - standard deviation & variance

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

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

Analyze and describe percentiles

Bivariate, scatter plots and correlation

Regression analysis

Equation of the best fit line

Apprenticeship and Workplace Mathematics 12 (MAT631K)

Measurement

Number

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

Ratios

Pythagorean theorem

Using the pythagorean relationship