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Master SAS Similarity Theorem: Prove Triangle Similarity

Derive proofs involving properties of angles and triangles

Classifying triangles

Isosceles and equilateral triangles

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

Solve problems involving properties of angles and triangles

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Unit circle

Angles in a circle

Determining non-permissible values for trig expressions

Solve problems involving cosine law and sine law, including ambiguous case

Law of sines

Ambiguous case: SSA triangles

Law of cosines

Applications of the sine law and cosine law

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

Null hypothesis and alternative hypothesis

Proving claims

Confidence levels, significance levels and critical values

Test statistics

Analyze puzzles and games involving spatial reasoning using problem-solving strategies

Line symmetry

Rotational symmetry and transformations

Solve problems involving application of rates

Direct variation

Identifying direct variations

Rate of change

Applications of linear relations

Solve problems involving scale diagrams using proportional reasoning

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Understand relationships among scale factors, areas, surface areas, and volumes of similar 2-D shapes and 3-D objects

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 involving systems of linear inequalities in two variables

Graphing linear inequalities in two variables

Graphing quadratic inequalities in two variables

Graphing systems of quadratic inequalities

Inequalities of combined functions

Inequalities of Combined Functions

Graphing systems of linear inequalities

Applications of inequalities

Demonstrate understanding of characteristics of 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

Adding functions

Subtracting functions

Multiplying functions

Dividing functions

Operations of Functions – In a Nutshell

Inverse functions

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

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

Confidence intervals to estimate population mean

Critically analyze society's use of inferential statistics

Traditional hypothesis testing

Traditional Mean Hypothesis Testing

P-value hypothesis testing

Proportion Hypothesis Testing

Mean hypothesis testing with t-distribution

Hypothesis Testing Mean Claims without Knowing <katex> \sigma </katex>

Mathematics 11

Logical Reasoning

Measurement

Relations and Functions

math

Intro

- Hi, welcome to this question right here. So, we have two similar triangles right here. That did tell us it's similar, right? So, don't worry about it. It is similar. We need to calculate the missing length. Turns out the missing length is right here, okay? 
So, what you do first is you have to set up like a proportional fraction. So, let's put an equal sign right here. And put up a fraction sign and a fraction sign. So, what you do is this, you know that these two are similar triangles, okay? So, the shorter side with the shorter side, there's a ratio that's involved between these two so, my own little preference is I'm gonna take the bigger number that goes first. So, I'm gonna put a two right here, for the bigger triangle. This side right here versus this side, which is 0.5, okay? 
Then, I'm gonna try to figure out my missing x right here. So, this missing x corresponds to the six over here, okay? 
Because the hypotenuse and the hypotenuse of the two triangles would go together. So, the six over here of my bigger triangle will match the x here for my little triangle. So once again, the bigger on the top, smaller on the bottom. Just because the math is easier. The six is over here, and the x is over here, okay? 
Now, maybe now you're not go with the algebra. But you can just think about this. They are the same ratio to each other. All you need to do is think about how to go from two to six. Well, mathematically, going from two to six, you just have to times it by three. And since you times by three to the top, you have to do the same thing to the bottom, right? 
So, 0.5 times by 3, you get yourself a 1.5 at the very end. So, x over here turns out just to be a 1.5 meters. And that is your final answer. Thanks for watching.

Learn how to determine similar triangles by using side-side-side (SSS) similarity, <a href='[[glossary.html|{"keyword":"SAS Similarity"}]]'>side-angle-side (SAS) similarity</a> and the properties of similar triangles to solve questions. It's always a good idea to refresh your memory on scale factors and proportions because we will be using them a lot in this lesson.

Identifying similar triangles

Ratios

Pythagorean theorem

Using the pythagorean relationship