geometry exam study guide – Flashcards
Unlock all answers in this set
Unlock answersquestion
Point
answer
A location
question
Does a point have length?
answer
NO
question
Does a point have width?
answer
NO
question
Does a point have thickness?
answer
NO
question
Line
answer
An infinite set of points that extends in two directions
question
Does a line have length?
answer
yes
question
Does a line have width?
answer
NO
question
Does a line have thickness?
answer
NO
question
Plane
answer
An infinite set of points that creates a flat surface that extends without ending
question
Does a plane have length?
answer
YES
question
Does a plane have width?
answer
YES
question
Does a plane have thickness?
answer
NO
question
Space
answer
the set of all points
question
colilinear
answer
points on the same line
question
noncollinear
answer
points not on the same line
question
coplanar
answer
points on the same plane
question
Noncoplanar
answer
points not on the same plane
question
segment
answer
a segment is named by giving its endpoints
question
ray
answer
named by giving its endpoint and another point
question
segment addition postulate
answer
If B is between A and C, then AB +BC = AC
question
congruent
answer
two objects that have the same size and shape are congruent
question
midpoint of the segment
answer
a midpoint divides a segment into two congruent segments
question
bisector of a segment
answer
a segment bisector is a line, segment, ray, or plane that intersects a segment at its midpoint
question
angle
answer
a figure formed by two rays with the same endpoint is an angle
question
vertex
answer
...
question
measure of an angle
answer
you can use a protractor to find the number associated with each side of an angle. To find the measure in degrees of an angle (m is greater than XYZ), compute the absolute value of the difference of these numbers
question
acute angle
answer
angle is greater than 0 and less than 90 degrees
question
obtuse angle
answer
greater than 90 degrees and less than 180 degrees
question
right angle
answer
angles= 90 degrees
question
straight angle
answer
angle = 180 degrees
question
angle addition postulate
answer
if a point Y lies in the interior of angle XOZ, then measurement of angle XOY + measurement of YOZ = measurement of angle XOZ
question
congruent angles
answer
two angles with equal measures are congruent: if measure of angle 5 = measure of angle 6, then angle 5 = angle 6
question
bisector of an angle
answer
the ray that divides an angle into two congruent angles is the angle bisector
question
adjacent angles
answer
coplanar angles with a common vertex and a common side but no common interior points are adjacent angles
question
postulate
answer
a basic assumption accepted without proof
question
theorem
answer
a statement that can be proved using postulates, definitions, and previously proved theorems
question
exists
answer
there is at least one
question
one and only one
answer
exactly one
question
determine
answer
to define or specify
question
relationships between points
answer
Two points must be collinear, three points may be collinear or noncollinear;Three points must be coplanar; three noncollinear points determine a plane; four points may be coplanar or noncoplanar;Four noncoplanar points determine space; space contains at least four non coplanar points
question
Three ways to determine a plane
answer
three noncollinear points determine a plane (pos 7); a line and a point not on the line determine a plane (theorem 1-2), two intersecting lines determine a plane (theorem 1-3)
question
relationships between two lines in the same plane
answer
either two lines are parallel, or they intersect in exactly one point
question
relationship between a line and a plane
answer
either a line and a plane are parallel, or they intersect in exactly one point, or the plane contains the line
question
relationships between two planes
answer
either two planes are parallel, or they intersect in a line
question
conditional statement (or conditional)
answer
written in if-then
question
what letter do they use for the hypothesis?
answer
p
question
what letter do they use for the conclusion?
answer
q
question
conditional statement
answer
if it is snowing, then it is cold?
question
p implies q
answer
it is snowing implies it is cold
question
p only if q
answer
it is snowing only if it is cold
question
q if p
answer
it is cold if it is snowing
question
converse
answer
of a conditional statement is formed by interchanging the hypothesis and the conclusion
question
conditional statement
answer
if p, then q (if today is Tuesday, then tomorrow is Wednesday)
question
converse
answer
if q, then p (if tomorrow is Wednesday, then today is Tuesday)
question
counterexample
answer
one way of proving a statement false is to give this
question
biconditional statement
answer
a statement combining a conditional and its converse
question
conditional statement
answer
if p, then q (if today is Tuesday, then tomorrow is Wednesday)
question
converse
answer
if q, then p (if tomorrow is Wednesday, then today is Tuesday)
question
biconditional
answer
p if and only if q (Today is Tuesday if and only if tomorrow is Wednesday)
question
midpoint theorem
answer
if M is the midpoint of AB, then AM = 1/2AB and MB =1/2AB
question
angle bisector theorem
answer
if BX is the bisector of angle ABC, then m of angle ABX = 1/2 measurement of angle ABC and measurement of angle XBC = 1/2 measurement of angle ABC
question
complementary angles
answer
two angles whose measure have the sum 90 are complementary
question
supplementary angles
answer
two angles whose measures have the sum 180 are supplementary
question
are vertical angles congruent?
answer
yes
question
perpendicular lines
answer
two lines that intersect to form right angles; biconditional (1) if two lines are perpendicular, then they form right angles (2) if two lines form right angles, then the lines are perpendicular
question
Properties of perpendicular lines
answer
1-if two lines are perpendicular, then they form congruent adjacent angles 2- if two lines form congruent adjacent angles, then the lines are perpendicular 3-if the exterior sides of two adjacent acute angles are perpendicular, then the angles are complementary
question
if two angles are supplements of congruent angles (or of the same angle, then what does it say about the two angles?
answer
they are congruent
question
If two angles are complements of congruent angles (or the same angle), what do you say aobut the two angles?
answer
they are congruent
question
parallel lines
answer
l is parallel to n if the lines are coplanar and they do not intersect
question
skew lines
answer
p and q are skew lines if they are not coplanar -skew lines are neither parallel not intersecting
question
Are skew lines parallel?
answer
no
question
Are skew lines intersecting?
answer
no
question
parallel planes
answer
plane N is parallel to plane M if they do not intersect. All planes are either parallel or intersecting.
question
all planes must be two things?
answer
parallel or intersecting
question
if two parallel lines are cut by a transversal
answer
then corresponding angles are congruent
question
if two parallel lines are cut by a transversal
answer
then alternate interior angles are congruent
question
if two parallel ones are cut by a transversal
answer
then same-side interior angles are supplementary
question
if a transversal is perpendicular to one of two parallel lines
answer
then it is perpendicular to the other one also
question
if two parallel lines are cut by a transversal, then ...
answer
corresponding angles are congruent, alternate interior angles are congruent AND same-side interior angles are supplementary
question
if a transversal is perpendicular to one of two parallel ones, then
answer
it is perpendicular to the other one also
question
if two lines are cut by a transversal and corresponding angles are congruent, then the lines are
answer
parallel
question
if two lines are cut by a transversal and alternate interior angles are congruent, then the lines
answer
are parallel
question
if two lines are cut by a transversal and same-side interior angles are supplementary, then the lines are
answer
parallel
question
in a plane two lines perpendicular to the same line are
answer
parallel
question
two lines parallel to a third line are
answer
parallel to each other
question
Ways to prove two lines parallel
answer
1. show that a pair of corresponding angles are congruent 2. show that a pair of alternate interior angles are congruent 3. show that a pair of same-side interior angles are supplementary 4. in a plane show that both lines are perpendicular to a third line 5. show that both lines are parallel to a third line
question
triangle
answer
the figure formed by three segments joining three noncollinear points
question
what are parts of a triangle
answer
vertices, sides, angles
question
how do you classify a triangle?
answer
the number of congruent sides
question
scalene triangle
answer
no sides are congruent
question
isosceles triangle
answer
at least two sides congruent
question
equilateral triangle
answer
all sides congruent
question
triangles can be classified by angles too
answer
...
question
acute triangle - how many angles?
answer
three acute angles
question
right triangle - how many angles?
answer
one right 90 degree angle
question
obtuse triangle - how many angles?
answer
one obtuse angle
question
equiangular triangle - what about the angles?
answer
all are congruent
question
the sume of the measures of the angles of a triangle =
answer
180 degrees
question
exterior angle
answer
the angle formed when one side of a triangle is extended
question
remote interior angle
answer
the two angles of the triangle not adjacent to the exterior angle
question
the measure of an exterior angle of a triangle =
answer
the sum of the measures of the two remote interior angles
question
polygons
answer
have vertices, sides, angles, and exterior angles
question
how do you name a polygon?
answer
by listing consecutive certices in order
question
diagonal
answer
a segment connecting two nonconsecutive vertices of a polygon
question
convex polygons
answer
polygons that no part of a diagonal is exterior to the polygon
question
3 sided polygon
answer
triangle
question
4 sided polygon
answer
quadrilateral
question
5 sided polygon
answer
pentagon
question
6 sided polygon
answer
hexagon
question
8 sided polygon
answer
octagon
question
10 sided polygon
answer
decagon
question
n sided polygon
answer
n-gon
question
the sum of the measures of the angles of a convex polygon with n sides =
answer
(n-2)180
question
the sum of the measures of the exterior angles of any convex polygon, one at each vertex =
answer
360
question
regular polygon
answer
a polygon that is both equiangular (all angles congruent) and equilateral (all sides congruent) is this kind of polygon
question
equiangular
answer
all angles congruent
question
equilateral
answer
all sides congruent
question
how many sides does a regular polygon have if the measure of each exterior angle is 60?
answer
...
question
how many sides does a regular polygon have if the measure of each interior angle is 160?
answer
...
question
inductive reasoning
answer
based on several past observations
question
conclusions based on inductive reasoning, are they always true?
answer
sometimes, but not always true
question
deductive reasoning
answer
based on accepted statements, including previous theorems, postulates, definitions, and given information
question
in deductive reasoning, the conclusion must be true if?
answer
the hypotheses are true
question
congruent
answer
if the same size and shape
question
two triangles are congruent if and only if ...
answer
their vertices can be matched up so corresponding parts (angles and sides) of the triangles are congruent
question
two polygons are congruent if and only if their vertices can be matched up so that corresponding parts are
answer
congruent
question
SSS postulate
answer
if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent
question
SAS postulate
answer
if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent
question
ASA postulate
answer
if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent
question
isosceles triangle theorem
answer
defined as having at least two sides congruent. they have special names for their parts. if two sides of a triangle are congruent, then the angles opposite those sides are congruent.
question
names of isosceles triangle parts
answer
legs, base, vertex angle, base angles
question
legs
answer
congruent sides of isosceles triangle
question
base
answer
the third side of isosceles triangle
question
vertex angle
answer
the angle opposite the base of isosceles triangle
question
base angles
answer
the angles adjacent tot he base of the isosceles triangle
question
if two angles of a triangle are congruent, then the sides opposite those angles are:
answer
congruent
question
If two angles of a triangle are congruent, then the sides opposite those angles are:
answer
congruent
question
other methods of proving triangles are congruent
answer
AAS theorem, HL theorem
question
AAS Theorem
answer
if two angles and non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent
question
HL Theorem
answer
If the hypotenuse and a leg of one right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent
question
All ways to prove two triangles are congruent (all triangles)
answer
1. SSS postulate 2. SAS postulate 3. ASA postulate 4. AAS theorem
question
WAys to prove two right triangles are congruent
answer
HL Theorem
question
median of a triangle
answer
a segment from a vertex of a triangle to the midpoint of the opposite side is a this
question
altitude of a triangle
answer
a segment from a vertex of a triangle perpendicular to the line that contains the opposite side is this
question
how many medians does every triangle have?
answer
3
question
how many altitudes does every triangle have?
answer
3
question
where are the medians of a triangle located?
answer
inside the triangle
question
where are the altitudes of a triangle located?
answer
inside, outside or part of the triangle
question
perpendicular bisector
answer
a line, segment, or ray perpendicular to a given segment at its midpoint is >>>> of the segment
question
a point lies on the perpendicular bisector of a segment if and only if the point is
answer
equidistant from the endpoints of the segment
question
a point lies on the bisector of an angle if and only if
answer
it is equidistant from the sides of the angle
question
distance from point to a line
answer
...
question
parallelogram
answer
a quadrilateral with both pairs of opposite sides parallel is this
question
opposite sides of a parallelogram are
answer
congruent
question
opposite angles of a parallelogram are
answer
congruent
question
diagonals of a parallelogram ...
answer
bisect each other
question
How to prove quadrilaterals are parallelograms?
answer
...
question
If both pairs of opposite sides of a quadrilateral are .....then the quadrilateral is a parallelogram
answer
congruent
question
if one pair of opposite sides of a quadrilateral are both ...then the quadrilateral is a parallelogram
answer
congruent and parallel
question
if the diagonals of a quadrilateral ......., then the quadrilateral is a parallelogram
answer
bisect each other
question
if both pairs of opposite angles of a quadrilateral are ..., then the quadrilateral is a parallelogram
answer
congruent
question
if three parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal
answer
...
question
a line that contains the midpoint of one side of a triangle and is parallel to another side passes through the midpoint of the third side
answer
if M is teh midpoint of XY and MN is parallel to YZ, then N is the midpoint of XZ
question
the segment that joins the midpoints of two sides of a triangle...
answer
1) is parallel to the third side 2) is half as long as the third side
question
rectangle
answer
quadrilateral with four right angles
question
a parallelogram because both pairs of opposite angles are congruent
answer
rectangle
question
rhombus
answer
a quadrilateral with four congruent sides
question
rhombus
answer
a parallelgram because both pairs of opposite sides are congruent
question
square
answer
a quadrilateral with four right angles and four congruent sides
question
square
answer
is a parallelogram, rectangle and a rhombus
question
rectangle
answer
has four right sides, all the properties of a parallelogram and has congruent diagonals
question
If one angle of a parallelogram is a right angle, then the parallelogram...
answer
is a rectangle
question
rhombus
answer
has four congruent sides, has all teh properties of a parallelogram, has diagonals that are perpendicular, and has diagonals that bisect its angles
question
if two consecutive sides of a parallelogram are congruent, then the parallelogram is a
answer
rhombus
question
square
answer
1- four right angles and four congruent sides 2- has all the properties of the parallelogram 3- has diagonals that are both congruent and perpendicular 4-has diagonals that bisect its angles
question
the midpoint of the hypotenuse of a right triangle is ...
answer
equidistant from the three vertices
question
trapezoids
answer
1- a quadrilateral 2- exactly one pair of parallel sides
question
isosceles trapezoid
answer
a trapezoid with congruent legs
question
trapezoid sides are called:
answer
parallel sides: bases other sides: legs
question
base angles of an isosceles trapezoid are
answer
congruent
question
median of a trapezoid
answer
the segment that joins the midpoints of the legs of the trapezoid
question
the median of a trapezoid:
answer
1-is parallel to the bases 2- has a length equal to the average of the base lengths
