# 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

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

angle that's 90º

180º

### horizontal

from east to west.

### verticle

from north to south.

--•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.

### 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

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

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.

a four-sided polygon.

### parallelogram

quadrilateral with both pairs of opp. sides parallel

### diagonal

segment joining two non-consecutive vertices of a polygon.

### 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

3 sides

4 sides

5 sides

6 sides

7 sides

8 sides

9 sides

10 sides

12 sides

### 2

____ points determine a line.

### 3

_____ points determine a plane.

Example: