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Similar Polygons: Definition, Examples, and Applications

Derive proofs that involve the properties of angles and triangles

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

Solve problems that involve the properties of angles and triangles

Classifying triangles

Isosceles and equilateral triangles

Solve problems that involve the cosine law and the sine law including the ambiguous case

Law of sines

Ambiguous case: SSA triangles

Law of cosines

Applications of the sine law and cosine law

auto-gen

Analyze and prove conjectures using inductive and deductive reasoning to solve problems

Set notation

Understanding How to Use Set Notation

Set builder notation

Intersection and union of 2 sets

Intersection and Union of 2 Sets

Intersection and union of 3 sets

Intersection and Union of 3 Sets

Factor by taking out the greatest common factor

Factor by taking out GCF

Factor by grouping

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

Analyze puzzles and games that involve spatial reasoning using problem-solving strategies

Line symmetry

Rotational symmetry and transformations

Surface area of 3-dimensional shapes

Arithmetic mean vs. Geometric mean

Solve problems that involve the application of rates

Applications of rational equations

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

Solve problems that involve scale diagrams using proportional reasoning

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Simplifying rational expressions and restrictions

Adding and subtracting rational expressions

Adding and Subtracting Rational Expressions

Multiplying rational expressions

Multiplying Rational Expressions

Multiplying Rational Expressions in Factored Form

Dividing rational expressions

Dividing Rational Expressions

Dividing Rational Expressions in Factored Form

Simplifying complex fractions

Demonstrate understanding of relationships among scale factors areas surface areas and volumes

Quadratic function in vertex form: y = a(x-p)^2 + q

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

Model and solve problems that involve systems of linear inequalities in two variables

Graphing linear inequalities in two variables

Graphing quadratic inequalities in two variables

Graphing systems of quadratic inequalities

Graphing systems of linear inequalities

Applications of inequalities

Demonstrate understanding of characteristics of quadratic functions

Introduction to quadratic functions

Characteristics of quadratic functions

Transformations of quadratic functions

Quadratic function in general form: y = ax^2 + bx + c

Converting from general to vertex form by completing the square

Shortcut: Vertex formula

Converting general form into vertex form by applying the vertex formula

Vertex Formula Application

Graphing quadratic functions: General form VS. Vertex form

Finding the quadratic functions for given parabolas

Applications of quadratic functions

Completing the square

Completing the Square

Research and give a presentation on a historical event or area of interest that involves mathematics

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

Arithmetic sequences

Arithmetic series

Arithmetic series formula

Geometric sequences

Geometric series

Geometric Series

Infinite geometric series

Demonstrate understanding of normal distribution including standard deviation and z-scores

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

Interpret statistical data using confidence intervals confidence levels and margin of error

Point estimates

Confidence levels and critical values

Margin of error

Margin of Error

Making a confidence interval

Grade 11 Applied Mathematics (30S)

Develop spatial sense

Develop logical reasoning

Develop spatial sense and proportional reasoning

Develop algebraic and graphical reasoning through the study of relations

Develop an appreciation of the role of mathematics in society

Develop statistical reasoning

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>


Finding the perimeter of a smaller quadrilateral using scale factors

Finding a missing side of a similar rectangle using scale factor

Testing if two triangles are similar by comparing side ratios

Determining if two polygons are similar using side ratios

Understanding scale factors for similar shapes

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

Similar Polygons: Understanding Geometric Proportions

What You'll Learn

Determine whether two polygons are similar by comparing side ratios

Calculate scale factors between similar polygons using corresponding sides

Apply scale factors to find unknown side lengths in similar figures

Distinguish between enlargements (scale factor > 1) and reductions (scale factor < 1)

Compute perimeters of similar polygons using proportional reasoning

What You'll Practice

Comparing side ratios to verify polygon similarity

Finding scale factors from corresponding side lengths

Calculating missing side lengths using given scale factors

Solving word problems involving similar rectangles and quadrilaterals

Why This Matters

Before You Start — Make Sure You Can:

This Unit Includes

5 Video lessons

Learning resources

Skills

Similar Polygons

Scale Factor

Ratios

Proportions

Enlargement

Reduction

Perimeter