Geometry Midterm Exam

104 terms by theresa8t8

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point

location represented by a dot, named by a capitol, print letter. ex: ˚A

line

straight, infinite <--------->

plane

a flat surface that goes on infinitely in all directions.

collinear

you can picture a line that could contain points <---•A---•B---•C--->

coplanar

you could picture a plane that'd contain all given points.

intersection

point where two lines meet

equidistant

equal in distance; distance from point to both objects is equal.

space

the set of all points

segment

two points on a line and all points between them.

ray

one end point, goes on infinitely in one direction

angle

made up of two rays, joined at a common end point

adjacent angles

must have a common vertex, common side, and no common interior points

congruent angles

two angles that have the same measure

congruent segments

segments that have equal lengths

angle bisector

ray that cuts an angle into two even angles

segment bisector

intercepts a segment at its midpoint

vertex

point connection two rays of an angle

acute angle

appears to be less that 90º

obtuse angle

greater than 90º but less than 180º

right angle

angle that's 90º

straight angle

180º

horizontal

from east to west.

verticle

from north to south.

segment addition postulate

--•X--•Y-------•Z-- XY+YZ=XZ

ruler postulate

used to find distance between two points by taking absolute value of difference of their coordinates.

protractor postulate

used to find measure of an angle.

angle addition postulate

angles must be adjacent

midpoint

point that divides the segment into two congruent segments

hypothesis

part of a conditional statement following "if" but not including the word "if." ex: "if you're a girl, then you're hot" the ____ is "you're a girl"

conclusion

part of conditional statement following "then" but not including the word "then." ex: "if Ke$ha were educated, then she should not be nearly as famous" the _____ is "she would not be nearly as famous."

conditional

statement with hypothesis and conclusion; if p, then q
p implies q
p only if q
q if p

converse

when we switch hypothesis and conclusion

counterexapmple

shows a conditional statement is false.

biconditional

both conditional and converse are both true. (all geometry definitions can be written as this).

complementary angles

two angles whose measures have the sum of 90º

vertical angles

two angles whose sides form two pairs of opposite rays and they are congruent angles

perpendicular lines

two lines that intersect to form a right angle

symmetric property

if 3=x, then x=3

transitive property

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

deductive reasoning

logical thinking where we use different postulates and theorems, definitions and properties to prove something.

parallel lines

lines that are on the same plane and don't intersect

skew lines

do not lie on the same plane and do not intersect

parallel planes

two or more planes that do not intersect

transversal

a line that intersects two or more times in different points

interior angles

angles that are between two lines

exterior angles

angles that are outside two lines

alternate interior angles

on opposite sides of transversal, formed with each of two lines

same-side interior angles

pair of angles between two lines and inside transversal

corresponding angles

same relative position

isosceles triangle

at least two sides are congruent

equilateral triangle

all sides are congruent

scalene triangle

no sides are congruent

equiangular

all angles of ∆ are congruent

auxilary line

a line that we add to a diagram to help us prove something.

remote interior

two interior angles that are not nest to an exterior angle

polygon

made up of line segments, joined only at endpoints.

convex polygon

does not intersect the interior

regular polygon

both equilateral and equiangular

diagnol

segment joining two non-consecutive verticals of a polygon

congruent

same size/shape

included angle

angle between congruent sides

SSS postulate

if 3 sides of one triangle are congruent to 3 sides of another triangle, triangles are congruent.

SAS postulate

if 2 sides and included angle of one ∆ are congruent to 2 sides and the included angle of another ∆, triangles are congruent.

ASA postulate

if 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another ∆, triangles are congruent.

AAS postulate

if 2 angles and a non-inclined side of 1 ∆ are congruent to 2 angles and non-inclined side of another ∆, triangles are congruent.

HL theorem

in 2 right triangles, the hypotenuse and leg are congruent to the hypotenuse and leg of the other triangle, triangles are congruent.

median

segment that joins a vertex to a midpoint of opposite side of a triangle.

isosceles triangle theorem

if 2 sides of a ∆ are congruent, then the angles opposite those sides are also congruent.

altitude

perpendicular segment from a vertex to line on opposite side of a ∆

perpendicular bisector

line that's perpendicular to a segment at its midpoint.

quadrilateral

a four-sided polygon.

parallelogram

quadrilateral with both pairs of opp. sides parallel

diagonal

segment joining two non-consecutive vertices of a polygon.

rectangle

quadrilateral with four right angles

rhombus

quadrilateral with four congruent sides

square

quadrilateral with four right angles and four congruent sides

trapezoid

quadrilateral with exactly one pair of parallel sides.

base of a trapezoid

parallel sides of a trapezoid are its base.

leg of trapezoid

nonparallel sides of a trapezoid are its legs.

isosceles trapezoid

legs are congruent and bases are congruent.

exterior angle inequality theorem

measure of an exterior angle of a ∆ is greater than the measure of either remote interior angle.

venn diagram

a circle diagram that may be used to represent a conditional.

converse

the ______ of the statement "if p, then q" is "if q then p"

inverse

if not p, then not p

contrapositive

if not q, then not p

equivalent

statement and contrapositive are logically equivalent. converse and inverse are logically equivalent.

indirect proof

a proof in which you 1) assume temporarily the opposite of what you're trying to prove. 2) Reason logically until you reach a contradiction of a known fact. 3) point out that the temp. assumption is false and that the conclusion is true.

temporary assumption

statement that asks to temporarily assume that the opposite of what you're trying to prove is true.

SAS inequality

if 2 sides of one ∆ are congruent to 2 sides of another ∆, but the included angle of the first ∆ is larger than the included angle of the second, the third side of the fist ∆ is longer than the third side of the second ∆

SSS inequality

if 2 sides of a ∆ are congruent to 2 sides of another ∆, but the third side of the first ∆ is longer than the third side of the second ∆, then the included angle of the first ∆ is larger that the included angle of the second ∆.

names the plane

single letter on the corner of a plane that does not represent a point does this:

coordinates

numbers on a number line

corresponding

if lines are parallel, the _____ angles are congruent

triangle

3 sides

quadrilateral

4 sides

pentagon

5 sides

hexagon

6 sides

heptagon

7 sides

octagon

8 sides

nonagon

9 sides

decagon

10 sides

dodecgon

12 sides

2

____ points determine a line.

3

_____ points determine a plane.

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