Download Geometry—Segment 2 Reference Sheet

Geometry—Segment 2 Reference Sheet
Module 6
Use distance formula and slope formula to classify triangles:
° Classifying by angles: acute, right, obtuse
° Classifying by sides: equilateral, isosceles, scalene
° Slope-intercept form: y=mx+b, where b is the y-intercept and m is the
slope.
° Point-slope form: y – y1 = m(x – x1) where (x1,y1) is a given point on the
line and m is the slope
° Parallel lines are two lines that lie within the same plane and never
intersect. Parallel lines have slopes that are equal.
° Perpendicular lines are two lines that intersect at 90-degree angles.
Perpendicular lines have slopes that are opposites and reciprocals and the
product of the slopes is always –1. (also, undefined and zero slope lines)
Properties of Parallelograms
- Both pairs of opposite sides
are congruent and parallel
- The diagonals bisect each
other
- Both pairs of opposite
angles are congruent
- Consecutive angles are
supplementary
Properties of Rectangles
- ALL PROPERTIES OF A
PARALLELOGRAM PLUS…
- Contains four right
angles
- The diagonals are
congruent
Properties of Squares
- ALL PROPERTIES OF A
RECTANGLE PLUS…
- All four sides are congruent
- The diagonals are
perpendicular
- The diagonals bisect the
angles
- Example of parallel lines: y= 2/3x + 2 and y= 2/3x –4.
- Example of perpendicular lines: y= 2/3x – 1 and y= -3/2x -3.
° Dividing segments into given ratio: The ratio 1:4 is read “one to four.” If you
were asked to find the distance that is at a ratio of 1:4 between two points, this
would mean the same as splitting the distance into 1 + 4 or 5 equal pieces and
then finding 1 of those pieces.
° Perimeter: the distance around the figure.
° Area of a polygon: the space inside the boundary of a 2-dimensional object
Properties of Rhombi
- ALL PROPERTIES OF A
SQUARE EXCEPT...
- Does NOT have four right
angles
- Does NOT have congruent
diagonals
Properties of Trapezoids
- Exactly one pair of parallel
sides
- Consecutive angles
between the bases are
supplementary
- Two special types: right
and isosceles
Properties of Kites
- Two pairs of adjacent, congruent
sides
- Non-vertex angles are congruent
- Diagonals are perpendicular
- Non-vertex diagonal is bisected
Module 7
SOH—CAH—TOA
Pythagorean Theorem
CHO—SHA—CAO
Angle of Elevation: an angle at
which an observer must direct his
or her line of sight in an upward
motion to view an object.
Angle of Depression: an angle at
which an observer must direct his
or her line of sight in a downward
motion to view an object.
Geometry—Segment 2 Reference Sheet
Module 8
° Volume: The ratio between the corresponding sides of two similar solids can be
represented in general terms by a:b (read "a to b") or a/b. The ratio of the volumes of similar solids can be represented by the ratio a 3:b3 or a3/b3 .
Circles
° Calculate circumference using: C = ∏d or C = 2∏r
° Calculate area using: A = ∏r2
° Percent of Change: change in dimensions can be represented by a scale
factor, a proportion, a ratio, or by a percent of change.
° Density: a ratio of mass to area or volume.
° Cavalieri’s Principle: if the area of the cross sections of two 3-D
figures are congruent and the height of the figures is also congruent,
then it can be concluded that the volumes of the two figures are
congruent.
Cone
° Volumecone = ⅓∏r2h
° Mass: how much matter is in an object
Cylinder
° Volumecylinder = ∏r2h
Sphere
° Volumesphere = 4/3∏r3
Module 9
° circle - the set of all points that are the same distance away from a fixed point
° radius - the distance between the center of a circle and any point on the circle
° chord - a segment on the interior of a circle whose endpoints are on the circle
Pyramid
° Volumepyramid = ⅓(B)(h)
° (B) Base = L x W
All circles have an equation. From its equation, we can determine
the center and the radius of the circle in order to graph it.
Equation of a Circle: (x–h)2 + (y–k)2 = r2 where (h, k) is the center
and r is the radius.
° diameter - a chord that passes through the center of the circle
° circumference - the distance around the circle
° secant - a line that intersects a circle in two places
° arc - one section of the circumference of a circle
° arc length - the distance between two points on a circle
° minor arc - an arc measuring less than 180°
A circumscribed circle is a circle
that surrounds a polygon and
intersects each one of its vertices.
Construct Perpendicular
Bisectors
An inscribed circle is a circle that is
contained within the interior of a polygon and intersects each side of a polygon exactly one time at a 90° angle.
Construct Angle Bisectors
Concentric Circles— Circles that share a
common center.
Arc Length = derived from the formula for the circumference of a circle.
Arc length = where x is the measure of the central angle.
Area of Sector = derived from the formula for the area of a circle.
Area of a sector = where x is the measure of the central angle.
Radians = Another unit of measure (other than degrees) to
Inscribed Quadrilateral Theorem =
The opposite angles of an inscribed
quadrilateral to a circle are supplementary.