# Geometry Midterm Vocab -McDowell

## 115 terms · all vocab and random stuff here and there from chapters 1-6.

### inductive reasoning

process of looking for patterns and making conjectures
-based on observations

### counter example

an example that shows a conjecture to be false
-specific

### point

has no dimension, but is usually represented by a small dot

### line

extends in 1 dimension
-usually represented by a straight line with arrows at each end
-has length
-never ends (infinite)

### plane

extends in 2 dimensions (has length and width), usually represented by a shape that looks like a wall or a table top
-also infinite

### collinear points

2 or more points that lie on the same line

### coplanar points

lie on the same plane

### line segment

has end points
-like a finite portion of an infinite line

### ray

has an initial point then in continues infinity

### opposite rays

have the same initial point, but go in opposite directions
-when looked at together, make line

### points of intersection

2 or more geometric figures intersect if they have 1 or more points in common

### postulate (axiom)

rule that is accepted without proof

### distance formula

d = square root of (x2-x1) squared + (y2-y1) squared

### angle

2 rays that have the same initial point

### 2 rays

sides of an angle

### vertex

shared initial point

### congruent angles

angles that have the same measure

### interior of an angle

between the points on each side of the angle

### exterior of an angle

points NOT on the sides or in the interior of an angle

### acute

less than 90 degrees

### right

exactly 90 degrees

### obtuse

between 90 and 180 degrees

### straight

exactly 180 degrees

common side and vertex, but no other interior points in common

### midpoint of a segment

point in the exact middle of a segment (cuts it in half)

cut in half

### segment bisector

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

### construction

geometric drawing that uses a limited set of tools (compass and straight edge)

### midpoint formula

for end points
-m = (x1 + x2 /2, y1 + y2/2)

### angle bisector

ray that divides an angle into 2 adjacent angles that are congruent

### vertical angles

two angles whose sides form 2 pairs of opposite rays (2 intersecting lines)
-shared vertex in middle

### linear pair

two adjacent angles whose non common sides are opposite rays

### complementary

two angles who measures add to exactly 90 degrees

### supplementary

two angles whose measures add to exactly 180 degrees
-all linear pairs are supplementary

### conjecture

an unproven statement based on observations

### endpoints

part of a line that consist of 2 points

starting point

### conditional statement

type of "logical" statement with 2 parts

### hypothesis

setup; comes after "if"

### conclusion

result; comes after "then"

### converse

formed by switching the hypothesis and conclusion of a conditional statement

### negation

writing the negative of a statement (not)

### inverse

formed by negating the hypothesis and conclusion of the original conditional statement

### contrapositive

formed by negating the hypothesis and conclusion of the converse

### definition

uses known words to describe a new word or concept

### perpendicular lines

lines that intersect to form right angles

### line perpendicular to a plane

that intersects a plane at a point so that it forms a right angle with every line in that plane

### biconditional statements

contain the phrase "if and only if" (Or IFF); same as writing a conditional statement and its converse together

### theorem

statement that follows as a result of other true statements
-must be proven

### two column proof

has numbered statements and reasons that show the logical order of an argument

### paragraph proof

proof written in paragraph form

### deductive reasoning

uses facts, definitions, and accepted properties in a logical order to write a logical argument

### parallel lines

coplanar, but never intersect

### skew lines

not coplanar, but never intersect

### parallel planes

2 or more planes that never intersect

### corresponding angles

occupy same positions on each parallel line

### alternate interior angles

between inside the 2 parallel lines, on opposite sides of transversal

### alternate exterior angles

between outside the 2 parallel lines, on opposite sides of transversal

### consecutive interior angles

between 2 parallel lines on same side of the transversal

### flow proof

uses arrows to show the flow of logical argument (reasons are usually written below the statements)

### slope

-rise/run
-change in y/change in x
-m = y2 - y1 / x2 - x1

### perpendicular slopes

have slopes that are negative reciprocals of each other

### transversal

line that intersects 2 or more parallel lines

### equilateral

all 3 sides are the same length

### isosceles triangle

triangle where at least 2 sides are congruent

### scalene triangle

triangle where all sides are different length

### acute triangle

all 3 angles are acute

### equiangular triangle

all 3 angles have the same measure

### obtuse triangle

1 angle is obtuse

### right triangle

1 angle is 90 degrees

### hypotenuse

the side opposite the right angle

2 sides of the triangle sharing a common vertex

### opposite side

the 3rd side of a triangle with adjacent sides

### legs

the 2 sides of a right triangle that make the right angle
-perpendicular to each other

### congruent figures

exactly same size and shape

### corresponding angles

angles in the same position

### corresponding sides

sides in the same position

### base angles

2 angles in an isosceles triangle that are adjacent to the base
-non congruent side

### vertex angle

in an isosceles triangle: angle opposite to the base; sides are the 2 congruent legs of the triangle

### coordinate proof

involves placing a geometric figure in the coordinate plane
-then we use distance and midpoint formulas long with postulates, theorems, etc, to prove statements

### perpendicular bisector

segment, line, or ray, that is perpendicular to a segment at its midpoint

### equidistant

the same distance from something

### distance from a point to a line

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

### perpendicular bisector of a triangle

a line, ray, or segment that is perpendicular to a side of the triangle at the midpoint of the side
-every triangle has 3
-all intersect at one point

### concurrent lines

3 or more lines that intersect at the same point

### point of concurrency

point where lines intersect at same point

### circumcenter

point of concurrency of the perpendicular bisectors of a triangle

### angle bisectors

bised the angles of a triangle
-every triangle has 3
-are concurrent

### incenter

point of concurrency of angle bisectors
-always inside the triangle
-equidistant from all 3 sides of the triangle

### median of a triangle

a segment whose endpoints are vertex of a triangle and the midpoint of the opposite side
-every triangle has 3
-are concurrent

### centroid

point of concurrency of medians of a triangle
-always inside the triangle
-balance point for the triangle

### altitude of a triangle

perpendicular segment from a vertex to the opposite side (or the line containing the opposite side)
-every triangle has 3
-are concurrent

### orthocenter

point of concurrency of altitude of a triangle
-acute triangle: inside
-right triangle: on the triangle, vertex of the right angle
-obtuse triangle: outside

### midsegment of a triangle

segment that connects the midpoints of 2 sides of a triangle

### indirect proof

prove a statement is true by first assuming that its opposite is true
-if assumption leads to an impossibility, then the original must be truel

### polygon

a plane figure formed by 3 or more segments so that each segment intersects exactly 2 others at each end point
-no curves, gaps, overlaps, or criss crosses

3 sides

4 sides

5 sides

6 sides

7 sides

8 sides

9 sides

10 sides

12 sides

### convex

no line containing a polygon side contains interior points

### concave

the extended line of at least 1 side contains points in the interior of the polygon

### regular polygon

polygon that is equilateral and equiangular

### diagonal of a polygon

segment that joins 2 nonconsecutive vertices

### parallelogram

a quadrilateral with both pairs of opposite sides parallel

### rhombus

all 4 sides are congruent
-equilateral parallelogram

### rectangle

all 4 angles are right angles
-equiangular parallelogram

### square

all 4 angles and all 4 sides are congruent
-equilateral and equiangular parallelogram (REGULAR)

### trapezoid

quadrilateral that has exactly one pair of opposite sides parallel

### kite

quadrilateral with 2 pairs of consecutive, congruent sides, but opposite sides are NOT parallel