Geometry—Segment 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

SOH—CAH—TOA 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

Circles

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

° Calculate area using: A = ∏r2

° 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.

Cylinder

° Volumecylinder = ∏r2h

Cone

° Volumecone = ⅓∏r2h

Sphere

° Volumesphere = 4/3∏r3

Pyramid

° Volumepyramid = ⅓(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: (x–h)2 + (y–k)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.