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Similar Polygons: Definition, Examples, and Applications

Grade 10 Math: Master Essential Skills & Concepts

1.1 Solving Problems Involving Similar Triangles

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Similar triangles

Similar polygons

Proportions

Proportions — Missing Denominator

Proportions — Missing Numerator

Proportions - Find the Missing Denominator LHS

Proportions - Find the Missing Denominator RHS

Proportions - Find the Missing Numerator LHS

Proportions - Find the Missing Numerator RHS

Combining the exponent rules

Isosceles and equilateral triangles

2.1 Solving Problems Involving the Trigonometry of Right Triangles

Use sine ratio to calculate angles and sides (Sin = o / h)

Use cosine ratio to calculate angles and sides (Cos = a / h)

Combination of SohCahToa questions

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

Use tangent ratio to calculate angles and sides (Tan = o / a)

Pythagorean theorem

Pythagorean Theorem

Using the pythagorean relationship

Applications of pythagorean theorem

3.1 Solving Problems Involving Surface Area and Volume, Using the Imperial and Metric Systems of Measurement

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

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

1.1 Manipulating and Solving Algebraic Equations

Slope intercept form:  y = mx + b

Slope intercept form: y = mx + b

General form:  Ax  + By  + C = 0

General form: Ax + By + C = 0

Introduction to linear equations

Special case of linear equations: Horizontal lines

Special case of linear equations: Vertical lines

2.1 Graphing and Writing Equations of Lines

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>

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

Graphing linear functions using table of values

Graphing linear functions using x- and y-intercepts

Graphing from slope-intercept form y=mx+b

Graphing linear functions using a single point and slope

Word problems of graphing linear functions

Rate of change

Parallel and perpendicular lines in linear functions

Applications of linear relations

3.1 Solving and Interpreting Systems of Linear Equations

Money related questions in linear equations

Unknown number related questions in linear equations

Distance and time related questions in linear equations

Rectangular shape related questions in linear equations

Determining number of solutions to linear equations

Solving systems of linear equations by graphing

Applications of linear equations

Solving systems of linear equations by elimination

Solving systems of linear equations by substitution

1.1 Manipulating Quadratic Expressions

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

Multiplying monomial by monomial

Multiply a Monomial by a Monomial

Multiplying monomial by binomial

Multiplying binomial by binomial

Multiplying polynomial by polynomial

2.1 Identifying Characteristics of Quadratic Relations

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

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

3.1 Solving Problems by Interpreting Graphs of Quadratic Relations

Applications of quadratic functions

Applications of quadratic equations

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Foundations of Mathematics, Grade 10, Applied (MFM2P) 

1. Measurement and Trigonometry

2. Modelling Linear Relations

3. Quadratic Relations of the Form y = ax^2 + bx + c

math

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Intro

- 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? 
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? 
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.

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