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Master Parallel and Perpendicular Line Segments | Geometry

NY.GEO-G.C.1

Central angles and proofs

NY.GEO-G.C.2a

Central and inscribed angles in circles

NY.GEO-G.C.2b

NY.GEO-G.C.5

auto-gen

Converting between degrees and radians

Trigonometric ratios of angles in radians

Radian measure and arc length

NY.GEO-G.CO.1

Line symmetry

Angles in a circle

Chord properties

Circles and circumference

Circle properties

Arcs of a circle

Areas and sectors of circles

Parallel and perpendicular line segments

Identifying Parallel Lines

Identifying Perpendicular Lines

NY.GEO-G.CO.10

Classifying triangles

Isosceles and equilateral triangles

NY.GEO-G.CO.11

Area and perimeter of parallelograms

2d shapes area and perimeter of parallelogram

2d shapes area and perimeter of parallelograms

NY.GEO-G.CO.12

Perpendicular bisectors

NY.GEO-G.CO.13

Inscribed angles and proofs

NY.GEO-G.CO.2

Rotational symmetry and transformations

Introduction to transformations

NY.GEO-G.CO.3

Horizontal and vertical distances

NY.GEO-G.CO.6

Congruence and congruent triangles

NY.GEO-G.CO.7

Triangles congruent by SSS proofs

NY.GEO-G.CO.8

Triangles congruent by SAS and HL proofs

Triangles congruent by ASA and AAS proofs

NY.GEO-G.CO.9

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

NY.GEO-G.GMD.1

Surface area and volume of prisms

Surface area and volume of cylinders

Surface area and volume of cones

NY.GEO-G.GMD.3

Surface area and volume of pyramids

NY.GEO-G.GMD.4

Surface area of 3-dimensional shapes

Introduction to surface area of 3-dimensional shapes

Nets of 3-dimensional shapes

NY.GEO-G.GPE.1a

Conics - Circle

NY.GEO-G.GPE.1b

NY.GEO-G.GPE.4

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)

Introduction to vectors

NY.GEO-G.GPE.5

Parallel line equation

Perpendicular line equation

Combination of both parallel and perpendicular line equations

NY.GEO-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>

NY.GEO-G.GPE.7

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

NY.GEO-G.MG.1

Scale diagrams

NY.GEO-G.MG.2

Word problems of polynomials

NY.GEO-G.SRT.1

Enlargements and reductions with scale factors

NY.GEO-G.SRT.2

Similar triangles

NY.GEO-G.SRT.4

Pythagorean theorem

Pythagorean Theorem

Estimating square roots

Using the pythagorean relationship

Applications of pythagorean theorem

NY.GEO-G.SRT.5

Similar polygons

NY.GEO-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)

NY.GEO-G.SRT.7

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

Cofunction identities

NY.GEO-G.SRT.8

Combination of SohCahToa questions

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

NY.GEO-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