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Master Parallel and Perpendicular Line Segments | Geometry

CA.G.G.C.1

Central angles and proofs

CA.G.G.C.2

Inscribed angles and proofs

CA.G.G.C.3

Circle chord, tangent, and inscribed angles proofs

CA.G.G.C.5

auto-gen

Converting between degrees and radians

Trigonometric ratios of angles in radians

Radian measure and arc length

Arcs of a circle

Areas and sectors of circles

CA.G.G.CO.1

Central and inscribed angles in circles

Parallel and perpendicular line segments

Identifying Parallel Lines

Identifying Perpendicular Lines

CA.G.G.CO.10

Isosceles and equilateral triangles

CA.G.G.CO.2

Rotational symmetry and transformations

Scale diagrams

Similar polygons

Introduction to transformations

CA.G.G.CO.4

Line symmetry

Perpendicular line proofs

CA.G.G.CO.6

Classifying triangles

Congruence and congruent triangles

CA.G.G.CO.8

Triangles congruent by SSS proofs

Triangles congruent by SAS and HL proofs

Triangles congruent by ASA and AAS proofs

CA.G.G.CO.9

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

CA.G.G.GMD.1

Circles and circumference

Circle properties

Surface area and volume of cylinders

Surface area and volume of cones

CA.G.G.GMD.3

Surface area and volume of pyramids

Surface area and volume of spheres

CA.G.G.GMD.4

Surface area and volume of prisms

CA.G.G.GPE.1

Conics - Circle

CA.G.G.GPE.2

Conics - Parabola

CA.G.G.GPE.4

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

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

CA.G.G.GPE.5

Parallel line equation

Perpendicular line equation

Combination of both parallel and perpendicular line equations

Parallel and perpendicular lines in linear functions

CA.G.G.GPE.6

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>

CA.G.G.MG.3

Word problems of polynomials

CA.G.G.S.CP.1

Organizing outcomes

Calculating Outcomes

CA.G.G.S.CP.2

Probability of independent events

CA.G.G.S.MD.6

Introduction to probability

Identify the Probability — Word Problem

Compound Probability

Reading Probability Models

Probability

CA.G.G.S.MD.7

Comparing experimental and theoretical probability

comparing experimental and theoretical probability

CA.G.G.SRT.1

Enlargements and reductions with scale factors

CA.G.G.SRT.10

Law of sines

Ambiguous case: SSA triangles

Law of cosines

CA.G.G.SRT.11

Applications of the sine law and cosine law

CA.G.G.SRT.2

Similar triangles

CA.G.G.SRT.4

Pythagorean theorem

Pythagorean Theorem

Estimating square roots

Using the pythagorean relationship

Applications of pythagorean theorem

CA.G.G.SRT.6

Use sine ratio to calculate angles and sides (Sin = o / h)

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

CA.G.G.SRT.7

Quotient identities and reciprocal identities

Pythagorean identities

Sum and difference identities

Sum and Difference Identities

Double-angle identities

Use cosine ratio to calculate angles and sides (Cos = a / h)

Cofunction identities

CA.G.G.SRT.8

Combination of SohCahToa questions

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

CA.G.G.SRT.8.1

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

CA.G.G.SRT.9

Area of triangles: 1/2 a*b sin(C)

math

Ex.1

Ex.2

Ex.3

Intro

In this lesson, we will learn:
<ul type = "disc">
<li>How to measure and draw angles using a protractor</li>
<li>How to identify whether pairs of lines or line segments are parallel or perpendicular</li>
</ul>

 Notes: 
<ul type = "disc">
<li>Protractors are used for measuring and drawing angles:</li>
</ul>

<center><img src="https://dmn92m25mtw4z.cloudfront.net/img_set/math7-6-1-x-1/v1/math7-6-1-x-1-529w.jpg" width="500" alt="Parallel and Perpendicular Line Segments"> </center>

<ul type = "circle">
<ul type = "circle">
<li>The middle of the flat side of the protractor goes on the vertex of the angle</li>
<li>There are two scales on the protractor from 0&deg; to 180&deg; (one going the clockwise way, one going the counter-clockwise way)</li>
<li>Line up one of the zeroes on the protractor with one arm of the angle and start measuring from 0&deg; until you reach the other arm</li>
</ul>
</ul>

<ul type = "disc">
 <li>Two lines or line segments can either intersect (cross) each other or be parallel. In this section, we will be learning how to identify and draw parallel and perpendicular line segments. <a href='[[glossary.html|{"keyword":"Parallel Lines"}]]'>Parallel line</a> segments never meet, no matter how far they are extended. Two line segments are perpendicular if they form a 90 <a href='[[glossary.html|{"keyword":"Degree","term":"Degree"}]]'>degree</a> angle where they cross. Parallel and perpendicular line segments are found everywhere in the world around us. For example, city planners often design roads to be parallel and perpendicular to each other. Along with roads, railroad tracks, lines on notebook paper, and bookcases are parallel.</li>
<ul type = "circle">
<li>When two figures are parallel with each other we can use the symbol: \(\parallel\)</li>
<li>When two figures are perpendicular with each other we can use the symbol: \(\perp\)</li>
</ul></ul>

<center><img src="https://dmn92m25mtw4z.cloudfront.net/img_set/math7-6-1-x-2/v1/math7-6-1-x-2-992w.jpg" width="600" alt="Points, Lines, Line Segments and Ra"> </center>

Parallel and perpendicular line segment basics