geometry H semester 1 final (smchs gahan)

chapter 1 - 7 (chapter five in seperate set)

point

a location in space

the defintion of a point is an exact location

false

line

a collection of points extending in opposite directions

plane

a collection of lines

undefined

point, line, plane

space (defined)

a set of all points

colinear points

points that are on the same line

coplanar points

points on the same plane

intersection

set of points in common

segment

part of a line with two endpoints

ray

part of a line with an ending point and extends in a single direction

opposite ray

two rays with the same starting point, but extend in opposite directions

segment addition pos

if B is between A and C then AB + BC = AC

congruency

1. same shape 2. same size

congurent segments

same length

midpoint

a point that divides a segment into two equal segments (Am = mB)

segment bisector

a line segment, ray, or plane that intersects a segment

angle

two rays with a common endpoint

angle addition pos

1. if point B lies within the interior of 2. two angles form 180 degrees

congruent angles

two angles that have the same measure

adjacent angles

two angles with


1. a common vertex
2. common side
3. con common interior points (no overlap)

bisector of an angle

bisector is a ray that divides the angle into two congruent adjacent angles

line (pts)

2 or more points

plane(pts)

3 or more points

space(pts)

4 or more points

through an two points is

exactly one line

through any three points is at least

one plane

if two pts are in a plane then the line that contains the points

is in that plane

if two planes intersect

then the intersection is a line

if two line intersect

then they intersect in exactly one pt

through a line and a pt not in the line is

exactly one plane

if two line intersect

then exactly one plane contains the lines

conditional

if-then statement

conditional symbolic

if p then q

counterexample

an example that makes the statement true but converse false

biconditional

when both the conclusion and its converse are true then it can be written as a single statement (all definitions are biconditionals)

addition property

if a = b and c = d then a+c = b+d

multiplication property

if a = b then c(a) = c(b)

reflexive property

a = a

transitive property

if a = b and b = c then a = c

midpoint thm

if M is the midpoint of seg. AB then AM = 1/2(AB)

angle bisector thm

if seg. BX is the bisector of

complementary <

two

supplementary <

two

vertical angles

angles with a common vertex and lines are opposite rays

vertical angle thm

vertical angles are congruent

perpendicular lines

two lines that intersect to form right angles

perpendicular lines form

congruent adjacent s

if two lines form con. adj

the lines are perpendicular

if the exterior sides of two adjacent angles are perpendicular then

the angles are complimentary

if two

the other two

parallel lines

two lines in the same plane that do not intersect

skew lines

two lines not in the same plane that do not intersect

parallel planes

two or more planes that do not intersect

if two lines do not intersect then the lines are parallel

false; lines can be skewed

transversal

a line cutting through two or more lines

if || planes pass through a plane then

the segments of intersection are congruent

corresponding angles (|| lines cut by transversal)

congruent

alt. int. angles (|| lines cut by transversal)

congruent

ss int. angles (|| lines cut by transversal)

supplementary

if a transversal is perpendicular to one of two || lines then

the transversal is also perpendicular to the second line

if a line is || to one of two || lines then

if must be || to the third line

five ways to prove || lines

1. congruent correspondings

through any pt not on a line there exists

exactly one line || to it

through any pt not on a line there exists

exactly one line perpendicular to it

scalene

no congruent sides

isosceles

at least two congruent sides

equilateral

three congruent sides

acute tri.

three acute angles

right tri.

one right angle (cannot have more than one right angle)

obtuse tri.

one obtuse angle

equilangular tri.

three congruent angles

auxillary lines

a line, ray, segment, or plane that is added to an illustration

the sum of three

180

in a triangle there can be at most one

right or obtuse <

the measure of the exterior of a tri. equals

the sum of the measures of the remote int s

polygon

a firgure with many

convexed polygon

lines only intersect at the side

non-convexed polygon

lines intersect not on sides

diagnols of a polygon

segments that joins non-adjacent vertices

calculating # of diagnols in polygon

(# of sides \* # of diagnols from one pt) / 2

calculating the sum of the interior

(# of sides - 2) \* 180

sum of exterior

360

regular polygon

1. congruent sides
2. congruent angles

calculating measure of each int <

((n-2) \* 180) / # of sides

calculating measure of each ext<

360 / # of sides

deductive reasoning

based on facts

inductive reasoning

based on observations

congruent triangles

two triangles where the 6 parts of correspondance are congruent

CPCTC

corresponding parts of congruent tirangles are congruent

5 ways to prove congruent triangles

1. SSS
2. SAS
3. ASA
4. AAS
5. HL

HL method

if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right tirangle then the triangles are congruent

a perpendicular line intersecting a plane is also

perpendicular to any line on that plane

if two sides of a triangle are congruent then

the opposite base

an equilateral triangle is also

equilangular

the bisector of the vertex < of an isosceles triangle is

perpendicular to the base at its midpoint

if triangles are congurent because of ASA they will also be congurent because of

AAS

median

a segment that joins a vertex to the midpt of the opposite side

point of concurrency

where medians intersect

medians always intersect

on the interior