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Mastering Rotational Symmetry and Transformations in 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

Intro

Ex. 1:

Ex. 2:

<p>- Hi, welcome to this question right here. So here we are. This figure right here, it says in the question it does have a rotation symmetry. So the first part of the question asks you, "Where is the center of rotation?" Now, all you have to do is just pick the center of your image and they have to know that this point, if you rotate it, it will form exactly the same image after you rotate it to certain degrees. So for this figure right here is a rectangular shape, the green part, right? So the center of the symmetry, or I'd say the center of rotation will be this point right here. So you can imagine that if you have a piece of paper with this size and if you rotate that piece of paper around, you will still get the same image, okay? So what are the order and the angle of rotation? The order of the rotation is this. You can actually relate the order to the line of symmetry you have. So if you look at the square right here, you have four symmetrical lines. You got one this way, this way, and this way, and then this way. So there's four lines. So technically the order of rotation for this question will be a four, okay? Now, the angle of rotation, you can actually calculate it. It's pretty simple. You see, when we rotate things around, it's actually 360. So to calculate this, it's 360 and all you have to do is divide it by the order number that you found, which is four. Now once again, to figure the order, all you have to do is figure a line of symmetry you have. So let's just quickly draw that. So we&apos;ve got one line going down this way. This is one symmetrical line and this is two and this is three and this is four. So with four lines of symmetry, you can actually relate that to the order number. So to calculate the angle of rotation, just take the 360, which is one complete turn, it's always 360 by the way, and divide it by four, the orders that you have. Now 360 divided by four, using your calculator, you get yourself a 90 degrees. So that's your angle of rotation right there, 90 degrees. It says, "Show your answers in degrees," which is this one right here and/or as a fraction of a turn. Now, a fraction of a turn, it's 360, right? So if you take that and divide it by 360, which is 90 divided by 360 again, basically you get yourself a one quarter, and this is your one quarter of a turn for this question. That's it. Thanks for watching.</p>


When an object is turned around its center of rotation to certain <a href='[[glossary.html|{"keyword":"Degree","term":"Degree"}]]'>degrees</a> and the object looks the same, we can say it has rotational symmetry. We will learn the details of rotational symmetry including, lines of symmetry, order of rotation, and angle of rotation.   