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Similar Polygons: Definition, Examples, and Applications

Solve problems requiring manipulation and application of formulas related to perimeter area Pythagorean theorem

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Evaluating polynomials

Solving polynomial equations

Word problems of polynomials

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)

Unknown number related questions in linear equations

Distance and time related questions in linear equations

Rectangular shape related questions in linear equations

Solving literal equations

Demonstrate understanding of Pythagorean theorem identify right triangle situations verify formula apply formula solve problems

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

Pythagorean theorem

Pythagorean Theorem

Using the pythagorean relationship

Applications of pythagorean theorem

Demonstrate understanding of similarity in convex polygons including regular and irregular polygons

Similar triangles

Similar polygons

Isosceles and equilateral triangles

Demonstrate understanding of primary trigonometric ratios apply similarity to right triangles generalize patterns apply ratios

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

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

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

Solve problems involving parallel perpendicular and transversal lines and pairs of angles formed between them

Parallel line equation

Perpendicular line equation

Combination of both parallel and perpendicular line equations

Parallel and perpendicular lines in linear functions

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

Demonstrate understanding of angles draw replicate construct bisect solve problems

Bearings and direction word problems

Bearings and Direction Word Problems

Angle of elevation and depression

Demonstrate understanding of SI system relationships between units for length, area, volume, capacity, mass, temperature

Upper and lower bound

Upper and Lower Bound

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

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

Demonstrate understanding of imperial system relationships between units for length, area, volume, capacity, mass, temperature

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

Imperial systems

Imperial Length Conversion

Solve and verify problems involving SI and imperial linear measurements including decimal and fractional measurements

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

Solve problems involving SI and imperial area measurements of regular, composite, and irregular 2-D shapes and 3-D objects

Midpoint formula: \(M = ( \frac{x_1+x_2}2  ,\frac{y_1+y_2}2)\)

Midpoint formula

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2  ,\frac{y_1+y_2}2)</katex>

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

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

Solve problems involving unit pricing and currency exchange using proportional reasoning

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

Direct variation

Identifying direct variations

Inverse variation

Money related questions in linear equations

Rate of change

Applications of linear relations

Ratios

Ratios - Find The Missing Value LHS

Ratios - Find The Missing Value RHS

Equivalent Ratios

Rates

Find the Biggest Rate 

Find the Unit Price 

Unit Rate Fill in Box

Find the Quickest Rate 

Unit Rate

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

Apprenticeship and Workplace Mathematics 10 (MAT421K)

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

Enlargements and reductions with scale factors

Scale diagrams