#### Study sets matching "geometry chapter 3"

#### Study sets matching "geometry chapter 3"

theorem 19

theorem 20

theorem 21

theorem unnumbered #1

all radii of a circle are congruent

if two sides of a triangle are congruent, the angles opposite…

if two angles of a triangle are congruent, the sides opposite…

if two sides of a triangle are not congruent, the the angles…

theorem 19

all radii of a circle are congruent

theorem 20

if two sides of a triangle are congruent, the angles opposite…

Alternate Interior Angles

Alternate Exterior Angles

Corresponding Angles

Consecutive Interior Angles

Angles that lie within a pair of lines and on opposite side o…

Angles that lie outside a pair of lines and on opposite sides…

Two angles that are formed by two lines cut by a transversal…

Angles that lie within a pair of lines and on the same side o…

Alternate Interior Angles

Angles that lie within a pair of lines and on opposite side o…

Alternate Exterior Angles

Angles that lie outside a pair of lines and on opposite sides…

if Consecutive Interior Angles are sup…

If Alternate Interior Angles are ≅, li…

if || lines are cut by a transversal,…

Vertical Angles Theorem

∠3 & ∠5 are supplementary

∠3 ≅ ∠6

Horizontal lines in the picture are ||. What tells us that ∠1…

∠1 ≅ ∠4

if Consecutive Interior Angles are sup…

∠3 & ∠5 are supplementary

If Alternate Interior Angles are ≅, li…

∠3 ≅ ∠6

Parallel lines

skew lines

Parallel planes

transversal

coplanar lines that do not interest

lines that do not interest and are not coplanar

planes that do not intersect

a line that intersect two or more coplanar lines at two diffe…

Parallel lines

coplanar lines that do not interest

skew lines

lines that do not interest and are not coplanar

parallel lines

skew lines

parallel planes

transversal

2 lines that are coplanar and do not intersect

2 lines that do not intersect and are not coplanar

2 planes that do not intersect

A line that intersects 2 or more coplanar lines at different…

parallel lines

2 lines that are coplanar and do not intersect

skew lines

2 lines that do not intersect and are not coplanar

Parallel Lines

Skew Lines

Parallel Planes

Transversal

Two or more lines in the same plane that do not intersect

Two or more lines that are in different planes and do not int…

Two or more planes that do not intersect

A line that intersects two other coplanar lines at two differ…

Parallel Lines

Two or more lines in the same plane that do not intersect

Skew Lines

Two or more lines that are in different planes and do not int…

Parallel Lines

Skew Lines

Parallel Planes

Transversal Line

Coplanar lines that do not intersect.

Lines that do not intersect and are not coplanar.

Planes that do not intersect.

A line that intersects two or more coplanar lines at two diff…

Parallel Lines

Coplanar lines that do not intersect.

Skew Lines

Lines that do not intersect and are not coplanar.

coinciding lines

intersecting lines

parallel lines

perpendicular lines

-same line... -have same slope... -have same y-intercept

-lines that intersect and have different slopes and different…

-have same slope... -have different y-intercepts

-have opposite reciprocal slopes... (slopes opposite)

coinciding lines

-same line... -have same slope... -have same y-intercept

intersecting lines

-lines that intersect and have different slopes and different…

Definition of Parallel Lines

Symbol used to denote two parallel lines

Parallel Planes

Skew Line

Two lines on the same plane that do not intersect.

Two planes that do not intersect

Two lines that do not intersect AND are not on the same plan.

Definition of Parallel Lines

Two lines on the same plane that do not intersect.

Symbol used to denote two parallel lines

parallel lines

perpendicular lines

skew lines

parallel planes

coplanar lines that do not intersect

two lines that intersect at 90 angles

lines that do not intersect and are not coplanar

planes that do not intersect

parallel lines

coplanar lines that do not intersect

perpendicular lines

two lines that intersect at 90 angles

If two angles are complementary to the…

Complementary Angles

Adjecent Angles

Linear Pairs

... then they are equal (congruent).

Two angles whose sum is 90 degrees.

These are angles that have a common vertex and a common side…

A pair of adjacent angles whose exterior sides form a straigh…

If two angles are complementary to the…

... then they are equal (congruent).

Complementary Angles

Two angles whose sum is 90 degrees.

parallel lines

perpendicular lines

skew lines

parallel planes

coplanar lines that do not intersect

lines that intersect at a 90 degree angle

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

planes that do not intersect

parallel lines

coplanar lines that do not intersect

perpendicular lines

lines that intersect at a 90 degree angle

The Reflexive Property

The Substitution Property

The Addition Property

The Subtraction Property

a = a.

If a = b, then a can be substituted for b in any expression.

If a = b, then a + c = b + c.

If a = b, then a - c = b - c.

The Reflexive Property

a = a.

The Substitution Property

If a = b, then a can be substituted for b in any expression.

Parallel Lines

Perpendicular Lines

Skew Lines

Parallel Planes

Two lines that lie in the same plane but do not intersect

Two lines that if they intersect they form a right angle

Two lines that do not lie in the same plane and they never in…

Two planes that do not intersect

Parallel Lines

Two lines that lie in the same plane but do not intersect

Perpendicular Lines

Two lines that if they intersect they form a right angle

Transversal

Alternate Interior Angles

Corresponding Angles

Same-Side Interior Angles

A line that intersects two coplanar lines at two distinct poi…

Angles that lie within (inside, in the interior) a pair of li…

Angles formed by a transversal cutting through 2 or more line…

Two interior angles on the same side of the transversal... If t…

Transversal

A line that intersects two coplanar lines at two distinct poi…

Alternate Interior Angles

Angles that lie within (inside, in the interior) a pair of li…

Parallel Lines

Vertical Angles

Supplementary Angles

Alternate Interior Angles

Coplanar lines that do not intersect

Two angles whose sides form two pairs of opposite rays

Two angles are supplementary if the sum of their measures is…

Nonadjacent interior angles that lie on opposite sides of the…

Parallel Lines

Coplanar lines that do not intersect

Vertical Angles

Two angles whose sides form two pairs of opposite rays

Slope means

Graph the following points on coordina…

Name the quadrant each of points are in:

Write the slope formula

rise/ run or the ______________ of a line

A- ... B- ... C- ... D- ... E- ... F-

m =

Slope means

rise/ run or the ______________ of a line

Graph the following points on coordina…

Parallel Lines

Perpendicular Lines

Skew Lines

Parallel Planes

Lines in the same plane that never intersect

Two lines that intersect to form right angles

Lines that do not intersect and are not coplanar

Planes that do not intersect

Parallel Lines

Lines in the same plane that never intersect

Perpendicular Lines

Two lines that intersect to form right angles

complementary angles

supplementary angles

adjacent angles

linear pair

Complementary angles are angles with measure that add to 90 d…

Supplementary angles are angles with measure that add to 180…

Adjacent angles are angles that have the same vertex, share a…

A linear pair is two adjacent angles who exterior sides form…

complementary angles

Complementary angles are angles with measure that add to 90 d…

supplementary angles

Supplementary angles are angles with measure that add to 180…

reflexive property

substitution property

addition property

subtraction property

a=a

if a=b, then a can be substituted for b in any expression

if a=b, then a+c=b+c

if a=b, then a-c=b-c

reflexive property

a=a

substitution property

if a=b, then a can be substituted for b in any expression

congruent triangles

congruent polygons

Reflexive Property

SSS postulate

all pairs of corresponding parts are congruent

all pairs of corresponding parts are congruent

Whenever a side or an angle is shared by two figures, we can…

If there exists a correspondence between the vertices of two…

congruent triangles

all pairs of corresponding parts are congruent

congruent polygons

all pairs of corresponding parts are congruent

If a transversal is perpendicular to o…

In a plane if 2 lines are perpendicula…

If 2 adjacent angles are complementary…

If exterior sides of 2 adjacent angles…

Perpendicular to Parallel Line Theorem

Perpenedicular to Parallel Line Theorem

Complementary Angles Theroem Converse

Complementary Angles Theroem

If a transversal is perpendicular to o…

Perpendicular to Parallel Line Theorem

In a plane if 2 lines are perpendicula…

Perpenedicular to Parallel Line Theorem

Transversal

Polygon

Convex Polygon

Concave Polygon

A line that intersects two coplanar lines at two distinct poi…

A closed shape with 3 sides that only intersect at endpoints

Has no diagonal with points outside the polygon

Has at least one diagonal with points outside the polygon

Transversal

A line that intersects two coplanar lines at two distinct poi…

Polygon

A closed shape with 3 sides that only intersect at endpoints

polygon

reflectional symmetry

axis of symmetry

equilateral

A closed figure formed by three or more line segments

When one half of a figure is a mirror image of the other half.

A line that divides a plane figure or a graph into two congru…

having all sides or faces equal

polygon

A closed figure formed by three or more line segments

reflectional symmetry

When one half of a figure is a mirror image of the other half.

Alternate Interior Angles

Alternate Exterior Angles

Corresponding Angles

Same Side Interior Angles

Nonadjacent interior that lie on opposite sides of a transver…

Nonadjacent exterior angles that lie on opposite sides of the…

Angles that lie on the same side of the traversal and in corr…

Interior angles that lie on the same side of the transversal.…

Alternate Interior Angles

Nonadjacent interior that lie on opposite sides of a transver…

Alternate Exterior Angles

Nonadjacent exterior angles that lie on opposite sides of the…

construct

sketch

draw

segment bisector

Making a shape through the use of a compass and straightedge.…

A free hand drawing

Making a shape through the use of your compass, straightedge,…

A line, ray, or segment that passes through the midpoint of a…

construct

Making a shape through the use of a compass and straightedge.…

sketch

A free hand drawing

Parallel Lines

Perpendicular Lines

Parallel Planes

Perpendicular Line to a Plane

Two or more lines which lie in the same plane and never inter…

Lines which intersect to form a right angle

Two or more planes which never intersect

A line that intersects a plane at a point and is perpendicula…

Parallel Lines

Two or more lines which lie in the same plane and never inter…

Perpendicular Lines

Lines which intersect to form a right angle

(2 intersecting lines form lin. Pair o…

perpendicular transversal theorem

(2 lines ⊥ to same line 2 lines ∥.)

distance from a point to a line

If two intersecting lines form a linear pair of congruent ang…

In a plane, if a transversal is perpendicular to one of the t…

If two coplanar lines are perpendicular to the same line, the…

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

(2 intersecting lines form lin. Pair o…

If two intersecting lines form a linear pair of congruent ang…

perpendicular transversal theorem

In a plane, if a transversal is perpendicular to one of the t…

alternate extirior angles

alternate interior angle

same side interior

same side extirior

non adjacent exterior angles that lie on opposite sides ot th…

non adjacent interior angles that lie on the opposite side of…

angle on the same side of the transversal and are inside the…

angle on the same side of the transversal but are outside the…

alternate extirior angles

non adjacent exterior angles that lie on opposite sides ot th…

alternate interior angle

non adjacent interior angles that lie on the opposite side of…

AA ~

congruent

proportional equation

SAS ~

If two angles of one triangle are congruent to the two corres…

Two shapes where there is a sequence of rigid transformations…

An equation stating that two ratios are equal.

If two triangles have two pairs of corresponding sides that a…

AA ~

If two angles of one triangle are congruent to the two corres…

congruent

Two shapes where there is a sequence of rigid transformations…

Parallel lines

Coplanar

Skew lines

Transversal

lines in the same plane that never intersect

points that lie on the same plane

Lines that do not intersect and are not coplanar

a line that intersects two or more lines

Parallel lines

lines in the same plane that never intersect

Coplanar

points that lie on the same plane

Transversal

Alternate Interior Angles

Corresponding Angles

Same-Side Interior Angles

A line that intersects two coplanar lines at two distinct poi…

Angles that lie within (inside, in the interior) a pair of li…

Angles formed by a transversal cutting through 2 or more line…

Two interior angles on the same side of the transversal... If t…

Transversal

A line that intersects two coplanar lines at two distinct poi…

Alternate Interior Angles

Angles that lie within (inside, in the interior) a pair of li…

Parallel Lines

Skew

Conciding

Parallel Postulate

Coplanar and does not intersect.

Noncoplanar and does not intersect.

Same line.

If there is a line and a point not on the line, then there is…

Parallel Lines

Coplanar and does not intersect.

Skew

Noncoplanar and does not intersect.

Transversal

Corresponding

Alternate Interior Angles

Alternate Exterior Angles

a line that intersects two or more lines.... Ex: Line t is the t…

Angles formed by a transversal cutting through 2 or more line…

Angles that can be found in between the two lines that are cu…

These are angles that can be found outside of the two lines t…

Transversal

a line that intersects two or more lines.... Ex: Line t is the t…

Corresponding

Angles formed by a transversal cutting through 2 or more line…

alternate exterior angles

alternate interior angles

axis of symmetry

center of a regular polygon

Two nonadjacent exterior angles that lie on opposite sides of…

Two nonadjacent interior angles that lie on opposite sides of…

A line that divides a planar figureinto two congruent reflect…

The point that is equidistant from all vertices of a polygon.

alternate exterior angles

Two nonadjacent exterior angles that lie on opposite sides of…

alternate interior angles

Two nonadjacent interior angles that lie on opposite sides of…

parallel lines

perpendicular lines

parallel planes

line perpendicular to a plane

lines in the same plane that never intersect

Lines that intersect to form right angles

planes that do not intersect

a line that intersects the plane in a point and is perpendicu…

parallel lines

lines in the same plane that never intersect

perpendicular lines

Lines that intersect to form right angles

Parallel lines

Skew lines

Alternate interior angles

Same side interior angles

Coplanar lines that do not intersect

noncoplanar and non parallel lines

nonadjacent interior angles that lie on opposite sides of the…

Interior angles that lie on the same side of the transversal

Parallel lines

Coplanar lines that do not intersect

Skew lines

noncoplanar and non parallel lines

Corresponding Angles Postulate - If tw…

Alternate Interior Angles Theorem - If…

Alternate Exterior Angles Theorem - If…

Same-Side Interior Angles Theorem - If…

then the pairs of corresponding angles are congruent.

then the alternate interior angles are congruent.

then the alternate exterior angles are congruent.

then the pairs of same-side interior angles are supplementary.

Corresponding Angles Postulate - If tw…

then the pairs of corresponding angles are congruent.

Alternate Interior Angles Theorem - If…

then the alternate interior angles are congruent.

a real number on a number line that ma…

a real number between any two given po…

one of the 360 marks in a 'circular pr…

all the positions through which a ray…

coordinate

distance

degree

rotation of rays

a real number on a number line that ma…

coordinate

a real number between any two given po…

distance

Segment bisector

Perpendicular bisector

Perpendicular Bisector Conjecture

Converse of the Perpendicular Bisector…

A line, ray, or segment that passes through the midpoint of a…

A segment that has many perpendiculars and many bisectors, bu…

If a point is on the perpendicular bisector of a segment, the…

If a point is equidistant from the endpoints of a segment, th…

Segment bisector

A line, ray, or segment that passes through the midpoint of a…

Perpendicular bisector

A segment that has many perpendiculars and many bisectors, bu…

Parallel Lines

Skew Lines

Parallel Planes

Transversal

coplanar lines that do not intersect

non coplanar lines (not parallel or intersecting)

Planes that do not intersect

the line that intersects two or more coplanar lines in differ…

Parallel Lines

coplanar lines that do not intersect

Skew Lines

non coplanar lines (not parallel or intersecting)

Segment bisector

Perpendicular bisector

Perpendicular Bisector Conjecture

Converse of the Perpendicular Bisector…

A line, ray, or segment that passes through the midpoint of a…

A line or segment that divides a line segment into two equal…

If a point is on the perpendicular bisector of a segment, the…

If a point is equidistant from the endpoints of a segment, th…

Segment bisector

A line, ray, or segment that passes through the midpoint of a…

Perpendicular bisector

A line or segment that divides a line segment into two equal…

Parallel Lines

Skew Lines

Transversal

Interior Angles

Coplanar lines that don't intersect ... II symbol

Non coplanar lines that don't intersect

Line that intersects 2 or more coplanar lines at distinct poi…

Formed by transversal that lie between 2 intersected lines

Parallel Lines

Coplanar lines that don't intersect ... II symbol

Skew Lines

Non coplanar lines that don't intersect