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Parallelograms: Properties, Diagonals, and Special Types

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

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 grouping

Factoring difference of squares: \(x^2 - y^2\)

Factoring trinomials

Solving quadratic equations by factoring

Solving quadratic equations by completing the square

Using quadratic formula to solve quadratic equations

Nature of roots of quadratic equations: The discriminant

Applications of quadratic equations

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: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

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

Slope equation: \(m = \frac{y_2-y_1}{x_2- x_1}\)

Slope intercept form:  y = mx + b

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

Triangles

Rectangles

Parallelograms

Trapezoids, rhombi, and kites

Polygons

Complex polygons

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

Law of cosines

Applications of the sine law and cosine law

Assignments

Challenge Zone

Foundation Review

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Principles of Mathematics, Grade 10, Academic (MPM2D)

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

2. Analytic Geometry

3. Trigonometry

math

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A clear explanation of parallelograms for geometry students: the definition, side and angle properties, diagonal relationships, symmetry, and how special parallelograms like rectangles, rhombi, and squares fit in, supported by worked examples.

Area and perimeter of parallelograms

Parallelograms | StudyPug

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Overview

Parallelogram Definition and Properties

What You'll Learn

Identify a parallelogram by its two pairs of parallel and congruent opposite sides.

Apply the rule that opposite angles in a parallelogram are always congruent.

Use the consecutive angles supplementary rule to find missing angle measures quickly.

Recognize that the diagonals of a parallelogram always bisect each other at their midpoint.

Compare special parallelograms such as rectangles, rhombi, and squares to a general parallelogram.

Solve algebraic problems involving unknown parallelogram side lengths, angles, and diagonal segments.

This Unit Includes

Learning resources