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

Post on 07-Feb-2018

213 views

Embed Size (px)

TRANSCRIPT

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.

Recommended