Download Geometry—Segment 2 Review

Geometry—Segment 2 Review
Module 6
° Convex polygons have all vertices pointed away from the center.
Concave polygons have at least one vertex pointing toward the center and at least one interior angle measuring more than 180 degrees.
° A regular polygon is a many-sided figure where the sides are all
equal in length and the angles have the same degree.
° Interior Angle Sum Theorem: the expression to find the sum of the
interior angles in a polygon is (n - 2) • 180° where ‘n’ represents the
number of sides . Divide the result ‘n’ to find a single angle measure
in a regular polygon.
° Exterior Angle Sum Theorem: the sum of the exterior angles of any
polygon total 360 degrees. You can find a single exterior angle
measure by dividing by the number of sides.
Module 7
Area Formulas
° Rectangle: A = lw
° Triangle: A = ½bh
° Parallelogram: A = bh
° Square: A = s2
° Rhombus & Kite: A = ½d1d2
° Trapezoid: A = ½h(b1 + b2)
° Regular Polygon: A = ½ap
where ‘a’ is the apothem
and ‘p’ is the perimeter
Module 8
° Important parts of a circle:
radius, chord, diameter,
circumference, arc (major
and minor), arc length,
secant, tangent
Vertex at
Circle Center
Tessellations & Symmetry
° Tessellation: a plane covered with a
pattern that repeats with no gaps or overlapping; a figure will tessellate if the sum
of its interior angles is divisible by 360
° Translational: pattern is moved ˄, ˅, ˂,
or ˃ without changing.
° Reflectional: pattern may be flipped over
a line without changing.
° Rotational: pattern may be turned about
a fixed point without changing.
° Glide Reflectional: pattern may be
moved and flipped without changing.
° Polyhedra: three-dimensional figures whose faces are polygons ; a prism has two bases and the lateral faces are rectangles;
a pyramid has one base and the lateral faces are triangles.
° Euler’s Formula: F + V - E = 2
° Lateral Area: the sum of the areas of the lateral faces in a figure
° LAprism = ph where ‘p’ is the perimeter of the base and ‘h’ is the
height of the prism
° LApyramid = ½pl where ‘p’ is the perimeter of the base and ‘l’ is
the slant height of the pyramid
Square
° S.A.prism = LA + 2B where ‘B’ is the area of the base
Pyramid
° S.A.pyramid: LA + B
Translations
(x, y) -> (x+1, y-2) sample
Reflections
x-axis: (x, y) -> (x, -y)
y-axis: (x, y) -> (-x, y)
line y=x: (x, y) -> (y, x)
Rotations
90 clockwise: (x, y) -> (y, -x)
90 counterclockwise:
(x, y) -> (-y, x)
180 : (x, y) -> (-x, -y)
Dilations
(x, y) -> (kx, ky)
where ‘k’ is the scale factor
Similarity Ratios
Rectangular
Prism
Triangular
Prism
° Calculate circumference using: C = ∏d or C = 2∏r
° Find arc length using the formula: Arc length = a/360 where ‘a; is the measure of
the central angle
° Calculate area using: A = ∏r2
° Find the area of a sector using: A = a/360 ∙ ∏r2
° The equation of a circle is represented by (x—h)2 + (y—k)2 = r2 where (h, k) is the
circle center and ‘r’ is the radius
Vertex
Vertex in Circle’s
Interior (not center)
Transformations Rules
Cylinder Formulas
° LAcylinder = 2∏rh
° S.A.cylinder = 2∏rh + 2∏r2
° Volumecylinder = ∏r2h
° ∏ = 3.14 or 22/7
Cone Formulas
° LAcone = ∏rl where ‘l’ is
the slant height
° S.A.cone = ∏rl + ∏r2
° Volumecylinder = ⅓∏r2h
outside Circle
Vertex
on Circle
Sphere Formulas
° S.A.sphere = 4∏r2
° Volumesphere = 4/3∏r3
Module 9
Sample Conditional Statement
If it is cloudy outside, then it is raining.
Inverse
Opposite of the original but in the same order
If it is not cloudy outside, then it is not raining.
Converse
Same as the original, but in a different order
If it is raining outside, then it is cloudy.
Contrapositive
(logically equivalent)
Opposite of the original AND in a different order
If it is not raining outside, then it is not cloudy.
Indirect Proof
° Assume the opposite of the original conclusion
° Examine each of the given statements relative to your assumption
° Find one FALSE statement to contradict the assumption which, in turn,
proves the original conclusion.
° Negation: stating the opposite of a statement
° Conjunction: statements that join two statements together usually with the word
“and”; must occur together
° Disjunction: statements that separate two statements, usually with the word “or;”
must occur separately
° Biconditional: statement in the form “if and only if”
Algebraic Properties
Example
Commutative (of addition and mult.) 3 + 2 + 5 = 5 + 2 + 3
Associative (of addition and mult.)
6 x 5 x 2 = (6 x 5) x 2
Distributive
4(x - 2) = 4x - 8
Symmetric
x = y and y = x
Transitive
If a = b and b = c, then a = c
Reflexive
x=x