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Master the Pythagorean Theorem: Applications and Examples

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

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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

Patterns

Patterns — Word Problem

Evaluating algebraic expressions

Evaluating Algebraic Expressions

Solving one - step equations:  x + a = b

1-step Equations

1-step Equations — Word Problem

Demonstrate understanding of angles by drawing, replicating, constructing, bisecting, and solving problems

Angles in a circle

Chord properties

Tangent properties

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

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

Solve problems involving unit pricing and currency exchange, using proportional reasoning

Rate of change

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

Representing percents

Representing Percents

Representing Percents — Word Problem

Representing Percents Two Graphs – Word Problem

Percents, fractions, and decimals

Conversion — Decimal to Fraction

Conversion — Decimal to Percent

Conversion — Fraction to Decimal

Conversion — Fraction to Percent

Conversion — Percent to Decimal

Conversion — Percent to Fraction

Percents – Word Problem

Convert a Decimal to a Fraction

Convert a Decimal to a Percent

Convert a Fraction to a Decimal

Convert a Fraction to a Percent

Convert a Percent  to a Decimal

Convert a Percent to a Fraction

Percents Fractions And Decimals – Word Problem

Percent of a number

Percent of a Number

percent of a number – Word Problem

Percent of a Number  Fraction Percent

Percent of a Number Integer Percent 

Percent of a number number With Decimal Percent 

Percent of a Number  Three Digits Number Percent

Adding and multiplying percents

Add and Multiply Percents — Word Problem

Add and Multiply Percents – Word Problem

Converting repeating decimals to fractions

Demonstrate understanding of transformations on a 2-D shape

Introduction to bearings

Bearings and direction word problems

Bearings and Direction Word Problems

Angle of elevation and depression

Line symmetry

Rotational symmetry and transformations

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

Solve problems involving right triangles using the Pythagorean theorem

Pythagorean theorem

Pythagorean Theorem

Using the pythagorean relationship

Applications of pythagorean theorem

Demonstrate understanding of primary trigonometric ratios by applying similarity to 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

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

Solve problems requiring manipulation and application of formulas related to trigonometric ratios

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

Grade 10 Essential Mathematics (20S) - Half Course 2

Develop critical thinking skills

Develop spatial sense

Develop skills to make informed consumer decisions

Develop spatial sense relating to triangles

math

Intro

In the previous section, we have learned the Pythagorean Theorem. We will now apply the knowledge to answer questions involving compound polygons.

Using the Pythagorean Relationship in math

Squares and square roots

Estimating square roots