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Mastering Rotational Symmetry and Transformations in Geometry

MA.912.GR.1.1

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

MA.912.GR.1.2

Classifying triangles

Congruence and congruent triangles

Triangles congruent by SSS proofs

Triangles congruent by SAS and HL proofs

Triangles congruent by ASA and AAS proofs

MA.912.GR.1.3

Isosceles and equilateral triangles

MA.912.GR.1.6

Similar triangles

Similar polygons

MA.912.GR.2.1

Rotational symmetry and transformations

MA.912.GR.2.2

Enlargements and reductions with scale factors

MA.912.GR.2.3

Scale diagrams

MA.912.GR.2.5

Introduction to transformations

Horizontal and vertical distances

MA.912.GR.2.6

Draw on coordinate planes

MA.912.GR.2.8

Cartesian plane

Cartesian Plane — Coordinates

MA.912.GR.3.1

auto-gen

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>

MA.912.GR.3.2

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

Point-slope form: y - y_1 = m(x - x_1)

MA.912.GR.3.3

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

MA.912.GR.4.1

Surface area of 3-dimensional shapes

MA.912.GR.4.2

Line symmetry

MA.912.GR.4.3

Introduction to surface area of 3-dimensional shapes

Nets of 3-dimensional shapes

MA.912.GR.4.5

Surface area and volume of prisms

Surface area and volume of pyramids

Surface area and volume of cylinders

Surface area and volume of cones

Surface area and volume of spheres

MA.912.GR.4.6

Surface area of prisms

Surface Area of Prisms Rectangle

Calculate the Surface Area

Surface area of cylinders

MA.912.GR.5.1

Metric systems

Add and Subtract Mixed Units

Metric Length Conversion

Add or Subtract Different Metric Units Convert to CM

Add or Subtract Different Metric Units Convert to M

Add or Subtract Different Metric Units Convert to MM

Imperial systems

Imperial Length Conversion

MA.912.GR.5.2

Conversions between metric and imperial systems

Metric to Imperial Conversions

Imperial to Metric Conversions

Conversions Between Metric and Imperial Systems Speed KM to MI

Conversions Between Metric and Imperial Systems Speed  MI to M

Metric-Imperial Length Conversion Inch To Cm

Metric-Imperial Length Conversion MM/CM/M/KM To FT

Metric-Imperial Length Conversion MM/CM/M/KM To MI

Conversions involving squares and cubic

Imperial to Metric Conversions — Squares and Cubes

Imperial Conversion — Squares and Cubes

Metric to Imperial Conversion — Squares and Cubes

Metric Area Conversion FT to CM

Metric Area Conversion Foot to Inch

Metric Area Conversion M/CM to Inch

MA.912.GR.5.3

Circles and circumference

Circle properties

MA.912.GR.6.1

Arcs of a circle

MA.912.GR.6.2

Areas and sectors of circles

Central angles and proofs

Inscribed angles and proofs

MA.912.GR.6.3

Central and inscribed angles in circles

Circle chord, tangent, and inscribed angles proofs

MA.912.GR.6.4

Angles in a circle

Chord properties

Tangent properties

MA.912.GR.7.2

Conics - Circle

MA.912.GR.7.3

Conics - Parabola

Conics - Ellipse

Conics - Hyperbola

MA.912.LT.4.10

Biconditionals

Deductive reasoning

Algebraic proofs

MA.912.LT.4.3

Inductive reasoning

Statements

Negations

Conjunctions and disjunctions

Truth tables

Conditionals

Inverses, converses, and contrapositives

MA.912.T.1.1

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)

MA.912.T.1.2

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

Pythagorean theorem

Pythagorean Theorem

Estimating square roots

Using the pythagorean relationship

Applications of pythagorean theorem

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.   