Geometry Honors Midterm

can not be defined using other figures.

• Point
• Line
• Plane

names a location and has no size. it is represented by a dot.

A capital letter

a straight path that has no thickness and extends forever

A lower case letter or two points on the line

• a flat surface that has no thickness and extends forever.
• a script capital letter
• or
• three points not on a line.

points that lie on the same line

points that do not lie on the same line

the part of a line consisting of two points and all points between them

a point at one end of a segment or the starting point of a ray

A capital letter

part of a line that starts at an endpoint and extends forever in one direction

It's endpoint and any other point

two rays that have a common endpoint and form a line

a statement that is accepted as true without proof

the set of all points the two or more figures have in common

a set of two or more equations containing two or more of the same variables

a number used to identify the location of a point

the absolute value of the difference of the coordinates

the distance between A and B

| a-b | or | b-a |

segments that have the same length

uses tick marks

the point that bisects, or divides the segment into two congruent segments

any ray, segment, or line that intersects a segment at its midpoint

a figure formed by two rays, or sides, with a common endpoint

a common endpoint

• Vertex
• a point on each ray and the vertex
• number

<R <SRT <1

the set of all points between the sides of the angle

the set of all points outside the angle

the absolute value of the difference of the real numbers that the rays correspond with on a protractor

measures greater than 0 degrees and less than 90 degrees

• Measures 90 degrees
• must have box

measures greater than 90 degrees and less than 180 degrees

• formed by two opposite rays
• measures 180 degrees

angles that have the same measure

a ray that divides an angle into two congruent angles

the (particular points) of all points in the interior of the angle that are equidistant from the sides of the angle

two angles in the same plane with a common vertex and a common side, but no common interior points

a pair of adjacent angles whose noncommon sides are opposite rays

two angles whose measures have a sum of 90 degrees

two angles whose measures have a sum of 180 degrees

90-x

180-x

two nonadjacent angles formed by two intersecting lines

the sum of the side lengths of the figure

• rectangle- 2l+2w
• square- 4s
• triangle a+b+c

the number of non overlapping square units of a given size that cover the figure

• rectangle- l*w
• Square side squared
• Triangle- 1/2bh
• circle- pi(r) squared

any side of a triangle

a segment from a vertex that forms a right angle with a line containing the base

• may be:
• inside the triangle (interior)
• outside (exterior)
• a side of the triangle

a segment that passes through the center of the circle and whose endpoints are on the circle

a segment whose endpoints are the center of the circle and a point on the circle

the distance around a circle

c=pi(d) or 2pi(r)

irrational

3.14 or 22/7

a plane that is divided into 4 regions by the x and y axis

m= (x₁+x₂ / 2, y₁+y₂ /2)

d= square root of (x₂-x₁)² + (y₂-y₁)²

• ONLY in a right triangle
• used to find distance
• a²+b²=c²

the 2 sides that form the right angle

the side across from the right triangle that stretches from one leg to the other

a change in the position, size, or shape of a figure

the original figure

the resulting figure

used to describe a transformation

used to label the image

a transformation across a line, called the line of reflection.

each points and its image are the same distance from the line of reflection

a transformation about a point P, called the center of rotation.

Each point and its image are the same distance from P

a transformation in which all the points of a figure move the same distance in the same direction

the process of reasoning that a rule or statement is true because specific cases are true

used to draw a conclusion from a pattern

• 1) look for a pattern
• 2) Make a conjecture
• 3) prove the conjecture or find a counterexample

a statement believed to be true based on inductive reasoning

an example that proves a conjecture false

a statement that can be written in the form "if p, then q"

p--> q

the part of p of a conditional statement following the word "if"

the part q of a conditional statement following the word, "then"

true or false of a conditional statement

false when the hypothesis is true and the conclusion if false

~p

the negation of a true statement is false, the negation of a false statement is true

statement formed by exchanging the hypothesis and conclusion

q-->p

statement formed by negating the hypothesis and the conclusion

~p--> ~q

statement formed by both exchanging and negating the hypothesis and conclusion

~q --> ~p

related conditional statements that have the same truth value

process of using logic to draw conclusions from given facts, definitions, and properties

a statement that can be written in the form, "p if and only if q" (iff)

if p, then q

if q, then p

used to write defintions

a statement that describes a mathematical object and can be written as a true biconditional

iff

closed plane figure formed by 3 or more line segments

each segment intersects exactly two other segments only at their endpoints

no two segments with a common endpoint are collinear

a three sided polygon

a 4 sided polygon

an argument that uses logic, definitions, properties, and previously proven statements to show that a conclusion is true

any statement that you can prove

proof that lists the steps of the proof in the left column and the matching reason in the right column.

1) write the conjecture to be proven

2) draw a diagram to represent the hypothesis of the conjecture

3) state the given information and mark it on the diagram

4) state the conclusion of the conjecture in terms of the diagram

5) plan your argument and prove the conjecture

uses boxes and arrows to show the structures of the proof

moves from left to right or top to bottom

justification written below the box

presents the steps of the proof and their matching reasons as sentences in a paragraph

coplanar and do not intersect

intersect at 90 degree angles.

are not coplanar, are not parallel, and do not intersect

planes that do not intersect

a line that intersects two coplanar lines at two different points

t

other 2 lines = r and s

lie on the same side of the transversal, on the same sides of lines r and s.

nonadjacent angles

lie on opposite sides of the transversal t, between lines r and s

lie on opposite sides of the transversal t

outside lines r and s

lie on the same side of the transversal

between lines r and s

a line perpendicular to a segment at the segment's midpoint

the length of the perpendicular segment from the point to the line

the difference in the y values of the 2 points on a line

the difference in the x values of 2 points on a line

the ratio of rise to run,

m= y₂-y₁ / x₂-x₁

a/b and -b/a

y-y₁=m(x-x₁)

x₁, y₁ is a given point on the line

y=mx+b

m=slope

b=y intercept

x=a

a= x intercept

y=b

b= y intercept

same slope, different y intercept

three acute sides

3 congruent acute angles

one right angle

one obtuse angle

three congruent sides

at least 2 congruent sides

no congruent sides

a line that is added to a figure to aid in a proof

-----------

a theorem whose proof follows directly from another theorem

set of all points inside the figure

the set of all points outside the figure

formed by 2 sides of a triangle

formed by one side of the triangle and the extension of an adjacent side

an interior angle that is not adjacent to the exterior angle

if the side lengths of a triangle are given, the triangle can have only one shape.

an angle formed by two adjacent sides of a polygon

the common side of 2 consecutive angles in a polygon

uses coordinate geometry and algebra

use the origin as a vertex, keeping the figure in Quad I

center the figure at the origin

center a side of the figure at the origin

use one or both axes as sides of the figure

angle formed by the legs

side opposite the vertex angle

2 angles that have the base as a side

a point is the same distance from 2 or more objects

three or more lines intersect at one point

the point where the lines intersect

the point of concurrency in a triangle

a circle that contains all the vertices of a polygon

the point of concurrency where the angle bisectors meet? (unsure)

intersects each line that contains a side of the polygon at exactly one point

the center of the triangle's inscribed triangle

always inside the triangle

a segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side

each triangle has 3 medians, which are concurrent

the point of concurrency of the medians of a triangle

always inside the triangle

center of gravity

perpendicular segment from a vertex to the line containing the opposite side

each triangle has 3 altitudes

can be inside, out, or on the triangle

miscellaneous shit

the point of intersection of the 3 altitudes of a triangle

segment that joins the midpoints if two sides of the triangle

every triangle has 3 midsegments, qhich form the midsegment triangle

1) identify the conjecture

2) assume the opposite of the conclusion is true

3) use direct reasoning to show that the assumption leads to a contradiction

4) conclude that since the assumption is false, the original conjecture is true