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Similar Polygons: Definition, Examples, and Applications

Grade 10 Math: Master Essential Skills & Concepts

1.1 Investigating the Basic Properties of Quadratic Relations

Characteristics of quadratic functions

Transformations of quadratic functions

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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

2.1 Relating the Graph of y = x^2 and Its Transformations

Combining transformations of functions

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

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

3.1 Solving Quadratic Equations

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

Solving quadratic equations by factoring

Solving quadratic equations by completing the square

Using quadratic formula to solve quadratic equations

Solving a quadratic equation with TWO REAL SOLUTIONS

Solving a quadratic equation with TWO COMPLEX SOLUTIONS

Nature of roots of quadratic equations: The discriminant

Applications of quadratic equations

Completing the square

Completing the Square

1.1 Using Linear Systems to Solve Problems

Determining number of solutions to linear equations

Solving systems of linear equations by graphing

Solving systems of linear equations by elimination

Solving systems of linear equations by substitution

System of linear equations

System of linear-quadratic equations

System of quadratic-quadratic equations

2.1 Solving Problems Involving Properties of Line Segments

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

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>

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 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

3.1 Using Analytic Geometry to Verify Geometric Properties

Parallel line equation

Perpendicular line equation

Combination of both parallel and perpendicular line equations

Parallel and perpendicular lines in linear functions

1.1 Investigating Similarity and Solving Problems Involving Similar Triangles

Similar triangles

Similar polygons

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

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

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)

3.1 Solving Problems Involving the Trigonometry of Acute Triangles

Law of sines

Ambiguous case: SSA triangles

Law of cosines

Applications of the sine law and cosine law

Get better math marks with our complete Grade 10 math help &ndash; be it <a href="http://www.edu.gov.on.ca/eng/curriculum/secondary/grades.html">Ontario math curriculum</a>, math curricula of <a href="https://curriculum.gov.bc.ca/curriculum/10-12#m">B.C.</a>, <a href="https://education.alberta.ca/mathematics-10-12/programs-of-study/">Alberta</a>, <a href="http://www.edu.gov.mb.ca/k12/cur/math/index.html">Manitoba</a>, <a href="https://www.curriculum.gov.sk.ca/webapps/moe-curriculum-BBLEARN/index.jsp?lang=en&subj=mathematics&level=foundations10">Saskatchewan</a>, <a href="http://www.ed.gov.nl.ca/edu/k12/curriculum/guides/mathematics/">Newfoundland</a>, or other provinces. We&apos;ve got you all covered!

Just like your class or textbook, our complete help for grade 10 math includes topics such as Trigonometry, Quadratic Equations, Radicals, Factoring polynomials, Linear equations, Linear systems, and more. Learn the concepts with our video tutorials that show you step-by-step solutions to even the hardest grade 10 math problems. Then, strengthen your understanding with tons of grade 10 math practice. 

All our lessons are taught by experienced grade 10 math teachers. Let&apos;s finish your homework in no time, and ACE that final.

Principles of Mathematics, Grade 10, Academic (MPM2D)

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

2. Analytic Geometry

3. Trigonometry

math

<h2>What is in grade 10 math?</h2>
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<h2>Is grade 10 math hard?</h2>
Not if you study hard! Like any other subject or grade level, grade 10 math questions and content come in various levels of difficulty. What some of you might find super easy the next person might find incredibly hard. To level the playing field, we offer you the greatest grade 10 math online course on the Internet! Let us do the heavy lifting and take that burden of anxiety off your back.
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<h2>How to pass grade 10 math?</h2>
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Begin with our grade 10 math lessons. Start here if you&apos;re feeling especially lost or confused about the topic. Watch these videos in no time and survey the 1000&apos;s of other lessons you may also require to understand the lesson. Some of these grade 10 math lessons are concomitant, so take the time to learn the core concepts before you move on to the next lesson. This may be the reason why you are struggling in the first place!
To give you a taste of what to expect in your grade 10 math test, we dedicate a good portion of our lessons taking you through step-by-step examples. We do this so that you are familiar with questions that you will see in your test or exam. Learn techniques to tackle similar kinds of questions and find out how to avoid making silly mistakes.
Finally, practice with our repository of 936 practice questions! This is a very important part of grade 10 math exam prep, so don&apos;t miss out on this! Test your knowledge and understanding of the topics and see how well you do in this mock test/exam. The more questions you do, the more prepared you&apos;ll be to pass grade 10 math with flying colours!
Stumped during practice? We&apos;re always here with 24/7 help so drop back into one our lessons and learn by example again!

<h2>How to prepare for grade 10 math?</h2>
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Throughout each lesson, don&apos;t forget to visit our bank of questions to help you sharpen your grade 10 math skills &ndash; challenge yourself each lesson to completing all the questions related to that chapter before moving on as this is the true test to seeing how prepared you are for grade 10 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.

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

Enlargements and reductions with scale factors

Scale diagrams