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Similar Polygons: Definition, Examples, and Applications

Demonstrate understanding of linear relations

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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

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

Parallel and perpendicular lines in linear functions

Applications of linear relations

Solve problems using sine law and cosine law

Introduction to bearings

Bearings and direction word problems

Bearings and Direction Word Problems

Angle of elevation and depression

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

Classifying triangles

Isosceles and equilateral triangles

Demonstrate understanding of transformations on 2-D shapes and 3-D objects

Line symmetry

Rotational symmetry and transformations

Enlargements and reductions with scale factors

Scale diagrams

Demonstrate understanding of limitations of measuring instruments

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

Addition rule for "OR"

Addition Rule for "OR"

Multiplication rule for "AND"

Multiplication Rule for "AND"

Conditional probability

Probability involving permutations and combinations

Solve problems involving vehicle acquisition by buying, leasing, and 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 viability of small business options considering expenses, sales, profit or loss

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

Analyze and interpret problems involving probability

Introduction to probability

Identify the Probability — Word Problem

Compound Probability

Reading Probability Models

Probability

Organizing outcomes

Calculating Outcomes

Probability of independent events

Comparing experimental and theoretical probability

comparing experimental and theoretical probability

Solve problems involving measures of central tendency

Median and mode

Median and Mode Table

Median and Mode – Word Problem

Median of an even length list

Median of an odd length list

Mean

Mean Word Problems

Find the Mean

Application of Means

Range and outliers

Range and Outlier Word Problems

Outlier Word Problems

Range Word Problems

Find the Range

Application of averages

Measures of Central Tendency — Word Problem

Find the Means — Data Tables

Find Mean and Mode — Data Table

Identify Outliers — Data Table

Analyze and describe percentiles

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

Mathematics at Work 12

Measurement

Number

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