geometry—segment 2 reference ??segment 2 reference sheet module 7 slope-intercept form: y=mx+b,...

Download Geometry—Segment 2 Reference  ??Segment 2 Reference Sheet Module 7  Slope-intercept form: y=mx+b, where b is the y-intercept and m is the slope

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  • GeometrySegment 2 Reference Sheet

    Module 7

    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)

    Classifying by angles: acute, right, obtuse

    Classifying by sides: equilateral, isosceles, scalene

    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 congru-

    ent

    - The diagonals are

    perpendicular

    - The diagonals bisect the

    angles

    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

    - 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

    Use distance formula and slope formula to classify triangles:

    Module 6

    Pythagorean Theorem

    SOHCAHTOA CHOSHACAO 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.

  • GeometrySegment 2 Reference Sheet

    Module 8

    Circles

    Calculate circumference using: C = d or C = 2r

    Calculate area using: A = r2

    Cavalieris 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.

    Cylinder

    Volumecylinder = r2h

    Cone

    Volumecone = r2h

    Sphere

    Volumesphere = 4/3r3

    Pyramid

    Volumepyramid = (B)(h)

    (B) Base = L x W

    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 vol-

    umes of similar solids can be represented by the ratio a3:b3 or a3/b3 .

    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.

    Mass: how much matter is in an object

    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

    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 poly-

    gon and intersects each side of a poly-

    gon exactly one time at a 90 angle.

    Construct Angle Bisectors

    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: (xh)2 + (yk)2 = r2 where (h, k) is the center

    and r is the radius.

    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 supple-

    mentary.

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