Math Semester Notes
Angles of Elevation:
Angle above the horizontal when looking up.
Used to calculate heights of objects.
Angles of Depression:
Angle below the horizontal when looking down.
Used to calculate depths of objects.
Soh Cah Toa:
Sine (Sin): Opposite/Hypotenuse.
Cosine (Cos): Adjacent/Hypotenuse.
Tangent (Tan): Opposite/Adjacent.
Used for non-right-angled triangles.
Relates the lengths of sides to the sines of their opposite angles.
Formula: a/sin(A) = b/sin(B) = c/sin(C).
Also used for non-right-angled triangles.
Relates the lengths of sides to the cosine of the included angle.
Formula:
a² = b² + c² - 2bc * cos(A).
b² = a² + c² - 2ac * cos(B).
c² = a² + b² - 2ab * cos(C).
Divides a segment into two equal parts.
Creates right angles.
Intersects at the midpoint.
Perpendicular segment from vertex to opposite side.
Can be inside, outside, or on the triangle.
Segment from vertex to midpoint of opposite side.
Divides triangle into two equal areas.
Divides angle into two equal angles.
Intersects at the incenter.
An Odd Peanut Butter Cup May Contain Apple Butter Instead:
Acronym for Angle Bisector, Perpendicular Bisector, Circumcenter, Median, Centroid, Altitude, Incenter.
Triangle Midsegment Theorem:
Midsegment is half the length of the parallel side.
Square:
All sides are equal.
All angles are right angles.
Diagonals bisect each other at right angles.
Rectangle:
Opposite sides are equal and parallel.
All angles are right angles.
Parallelogram:
Opposite sides are equal and parallel.
Opposite angles are equal.
Rhombus:
All sides are equal.
Opposite angles are equal.
Trapezoid:
One pair of opposite sides are parallel.
Non-parallel sides have different lengths.
Triangles: ½ Bh
Parallelograms: Bh
Trapezoids: ½ (b1+b2)h
Rhombus/Kites: 1/2(d*d)
Circles: pi r squared
Polygons: ½ ap
Prisms:
LSA- ph
TSA- ph + 2b
Cylinders:
LSA- 2pi rh
TSA- 2 pi rh + 2 pi r squared
Pyramids:
LSA- ½ pl
TSA- ½ pl + b
Cones:
LSA- pi r l
TSA- pi r l + pi r squared
Spheres
TSA- 4 pi r squared
1/2- 3 pi r squared
Cylinder: V = πr²h
Prism: V = Bh (B = base area)
Pyramid: V = (1/3)Bh
Cone: V = (1/3)πr²h
Sphere: V = (4/3)πr³
Arc Length Formula: arc/360 = x/pi d
Sector Area Formula: arc/360 = x/pi r squared
Segment Area Formula: sector area - triangle area
Properties of Radii and Chords: Equal chords have equal arcs
Properties of Tangents: Tangents from a point are equal in length
Angles of Elevation:
Angle above the horizontal when looking up.
Used to calculate heights of objects.
Angles of Depression:
Angle below the horizontal when looking down.
Used to calculate depths of objects.
Soh Cah Toa:
Sine (Sin): Opposite/Hypotenuse.
Cosine (Cos): Adjacent/Hypotenuse.
Tangent (Tan): Opposite/Adjacent.
Used for non-right-angled triangles.
Relates the lengths of sides to the sines of their opposite angles.
Formula: a/sin(A) = b/sin(B) = c/sin(C).
Also used for non-right-angled triangles.
Relates the lengths of sides to the cosine of the included angle.
Formula:
a² = b² + c² - 2bc * cos(A).
b² = a² + c² - 2ac * cos(B).
c² = a² + b² - 2ab * cos(C).
Divides a segment into two equal parts.
Creates right angles.
Intersects at the midpoint.
Perpendicular segment from vertex to opposite side.
Can be inside, outside, or on the triangle.
Segment from vertex to midpoint of opposite side.
Divides triangle into two equal areas.
Divides angle into two equal angles.
Intersects at the incenter.
An Odd Peanut Butter Cup May Contain Apple Butter Instead:
Acronym for Angle Bisector, Perpendicular Bisector, Circumcenter, Median, Centroid, Altitude, Incenter.
Triangle Midsegment Theorem:
Midsegment is half the length of the parallel side.
Square:
All sides are equal.
All angles are right angles.
Diagonals bisect each other at right angles.
Rectangle:
Opposite sides are equal and parallel.
All angles are right angles.
Parallelogram:
Opposite sides are equal and parallel.
Opposite angles are equal.
Rhombus:
All sides are equal.
Opposite angles are equal.
Trapezoid:
One pair of opposite sides are parallel.
Non-parallel sides have different lengths.
Triangles: ½ Bh
Parallelograms: Bh
Trapezoids: ½ (b1+b2)h
Rhombus/Kites: 1/2(d*d)
Circles: pi r squared
Polygons: ½ ap
Prisms:
LSA- ph
TSA- ph + 2b
Cylinders:
LSA- 2pi rh
TSA- 2 pi rh + 2 pi r squared
Pyramids:
LSA- ½ pl
TSA- ½ pl + b
Cones:
LSA- pi r l
TSA- pi r l + pi r squared
Spheres
TSA- 4 pi r squared
1/2- 3 pi r squared
Cylinder: V = πr²h
Prism: V = Bh (B = base area)
Pyramid: V = (1/3)Bh
Cone: V = (1/3)πr²h
Sphere: V = (4/3)πr³
Arc Length Formula: arc/360 = x/pi d
Sector Area Formula: arc/360 = x/pi r squared
Segment Area Formula: sector area - triangle area
Properties of Radii and Chords: Equal chords have equal arcs
Properties of Tangents: Tangents from a point are equal in length