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Geometry Angles1

MathematicsGrade 12Grade 11Grade 10Grade 6Grade 7Grade 8Grade 9

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Geometry Angles

DESCRIPTION

A shape, formed by two lines or rays diverging from a common point (the vertex).

HOW TO:

Acute = <90 Degrees

Right = 90 Degrees

Obtuse = >90 Degrees

Everyday Use

Angles are used daily in solving geometry problems

Lyrics

 

 

I found my Angle 

 

Verse 1 

 

Let’s start with naming, two points A and C// 

Rays through each the vertex is the place they meet// 

Lets call that point B, and the angle ABC// 

And or CBA or just angle B, stay with me//  

Use a protractor to count degrees// 

And angle is right if an angle is 90// 

Obtuse if its bigger and acute if its tiny-er// 

That’s how we classify the angles that we’re finding// 

Parallel lines are two lines that will never meet// 

Intersecting lines meet at one point only// 

If they’re perpendicular they intersect to make a T// 

And or a right angle, and or 90 degrees// 

Any polygon with three sides and three vertices// 

Is called a tri-angle, I’m sure you’ve probably heard of these// 

Equal sides sometimes, equal angles maybe// 

Just remember all three angles equal 180, baby// 

 

 

 

Verse 2 

 

Now onto polygons, yea you know shapes// 

Connecting lines creating sides, octagons have eight// 

Heptagons have seven, hexagons have six// 

Pentagons have five, “nona”s nine, “deca”s ten// 

Quadrilaterals have four, triangles have three// 

So many of each, but each is so unique. Look at these// 

Squares have four right angles, rectangles only two inside// 

A rhombus has four equal sides and Trapezoids two parallel lines// 

Two equal sides in a triangle, it’s isosceles//  

And its right if an angle is 90 degrees// 

If no sides are equal than it’s scalene// 

And the square of C’s the square of A plus square of B// 

That theory is Pythagorean//  

And in the case of polygons it’s a similar theme// 

We can find the 4th angle with the first three// 

because an equilateral’s angles equal 360//  

 

Standards

  • CCSS.MATH.CONTENT.6.G.A.3 — Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.
  • CCSS.MATH.CONTENT.6.G.A.1 — Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
  • CCSS.MATH.CONTENT.8.G.A.5 — Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.
  • CCSS.MATH.CONTENT.8.G.A.1.B — Angles are taken to angles of the same measure.
  • CCSS.MATH.CONTENT.HSF.TF.A.1 — Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
  • CCSS.MATH.CONTENT.7.G.A.3 — Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.
  • CCSS.MATH.CONTENT.7.G.B.5 — Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
  • CCSS.MATH.CONTENT.6.SP.B.5.B — Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
  • CCSS.MATH.CONTENT.HSF.TF.A.2 — Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.
  • CCSS.MATH.CONTENT.6.G.A.2 — Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.
  • CCSS.MATH.CONTENT.HSF.TF.A.4 — (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
  • CCSS.MATH.CONTENT.HSF.TF.A.3 — (+) Use special triangles to determine geometrically the values of sine, cosine, tangent for ?/3, ?/4 and ?/6, and use the unit circle to express the values of sine, cosine, and tangent for x, ? + x, and 2? - x in terms of their values for x, where x is any real number.
  • CCSS.MATH.CONTENT.HSF.TF.C.8 — Prove the Pythagorean identity sin2(?) + cos2(?) = 1 and use it to find sin(?), cos(?), or tan(?) given sin(?), cos(?), or tan(?) and the quadrant of the angle.
  • CCSS.MATH.CONTENT.7.G.A.2 — Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
  • CCSS.MATH.CONTENT.6.G.A.4 — Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.
  • CCSS.MATH.CONTENT.6.SP.B.5.A — Reporting the number of observations.