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inscribed angle

theorem 9-7

corollary 1

corollary 2

an angle whose vertex is on a circle and whose sides contain…

the measure of an inscribed angle is equal to half the measur…

if 2 inscribed angles intercept the same arc, then the angles…

an angle inscribed in a semicircle is a right angle

inscribed angle

an angle whose vertex is on a circle and whose sides contain…

theorem 9-7

the measure of an inscribed angle is equal to half the measur…

Point

Line

Plane

Collinear Points

Undefined term... Has no dimensions ... Represented by a small dot

Undefined term... Extends in one dimension ... Straight w/o curve

Undefined term ... Extends in two dimensions ... Represented by a s…

Points that lie on the same line

Point

Undefined term... Has no dimensions ... Represented by a small dot

Line

Undefined term... Extends in one dimension ... Straight w/o curve

complementary angles

supplementary angles

congruent

vertical angles

two angles whose measures have a sum of 90 degrees

two angles whose measures have a sum of 180 degrees

two angles that have equal measure

two opposite angles formed by two intersecting lines

complementary angles

two angles whose measures have a sum of 90 degrees

supplementary angles

two angles whose measures have a sum of 180 degrees

Definition of Congruence

Definition of Right Angle

Definition of Straight Angle

collinear

If two segments or angles are congruent, then they are equal…

If an angle's measure is 90 degrees, then it is a right angle.

If an angle's measure is 180 degrees, then it is a straight a…

points that lie on the same line

Definition of Congruence

If two segments or angles are congruent, then they are equal…

Definition of Right Angle

If an angle's measure is 90 degrees, then it is a right angle.

Angle

Sides

Vertex

Acute Angle

The space (usually measured in degrees) between two intersect…

A line bounding a plane figure.

A meeting point of two lines that form an angle.

An angle smaller than a right angle (it is less than 90 degre…

Angle

The space (usually measured in degrees) between two intersect…

Sides

A line bounding a plane figure.

angle

interior

exterior

congruent angles

A/n ______ is made up of two rays that share a common endpoin…

The space inside an angle.

The space outside the angle.

Angles with the same measure.

angle

A/n ______ is made up of two rays that share a common endpoin…

interior

The space inside an angle.

Arc

Intercepted arc

Minor Arc

Major Arc

Points on the circle and in between two identified points

Created by an angle intersecting the circle

Arc created by an angle less than 180 degrees

Arc created by an angle over than 180 degrees

Arc

Points on the circle and in between two identified points

Intercepted arc

Created by an angle intersecting the circle

parallel lines

congruent objects

vertical angles

perpendicular lines

two lines that do not intersect and are coplanar; have the sa…

two objects that have exactly the same size and shape; pairs…

two nonadjacent angles formed by two intersecting lines

two lines that intersect to form a right angle

parallel lines

two lines that do not intersect and are coplanar; have the sa…

congruent objects

two objects that have exactly the same size and shape; pairs…

triangle angle sum theorum

right triangle corollary

angle corollary

exterior angle

the sum of the interior angles of a triangle is 180 degrees

in a right triangle, the two acute angles are complementary

there can be at most one right or one obtuse angle in a trian…

an angle formed by extending the side of the triangle

triangle angle sum theorum

the sum of the interior angles of a triangle is 180 degrees

right triangle corollary

in a right triangle, the two acute angles are complementary

Complementary Angles

Supplementary Angles

Vertical Angles

Linear Pair

Two angles whose sum is 90 degrees.

Angles whose sum is 180 degrees.

A pair of opposite congruent angles formed by intersecting li…

A pair of adjacent angles whose non-adjacent sides form oppos…

Complementary Angles

Two angles whose sum is 90 degrees.

Supplementary Angles

Angles whose sum is 180 degrees.

B

D

E

B

A - Alt. Int. Angles... B - Alt. Ext. Angles... C - Corresponding A…

A - Alt. Int. Angles... B - Alt. Ext. Angles... C - Corresponding A…

A - Alt. Int. Angles... B - Alt. Ext. Angles... C - Corresponding A…

A - Alt. Int. Angles... B - Alt. Ext. Angles... C - Corresponding A…

B

A - Alt. Int. Angles... B - Alt. Ext. Angles... C - Corresponding A…

D

A - Alt. Int. Angles... B - Alt. Ext. Angles... C - Corresponding A…

linear: 180

trigonal planar: 120

tetrahedral: 109.5

bent: 120

Lone Pairs: 0, Bonded Atoms: 2

Lone Pairs: 0, Bonded Atoms: 3

Lone Pairs: 0, Bonded Atoms: 4

Lone Pairs: 1, Bonded Atoms: 2

linear: 180

Lone Pairs: 0, Bonded Atoms: 2

trigonal planar: 120

Lone Pairs: 0, Bonded Atoms: 3

Parallel lines

Skew lines

Parallel planes

Transversal

Lines that are coplanar and do not intersect

Lines that are not co-planner and do not intersect

Planes that do not intersect

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

Parallel lines

Lines that are coplanar and do not intersect

Skew lines

Lines that are not co-planner and do not intersect

Parallel lines (ll)

Perpendicular lines (⊥)

Skew lines

Parallel planes

- parallel lines are coplanar and do not intersect

- perpendicular lines intersect at 90 ° angles

- skew lines are not coplanar, not parallel, and do notn inte…

- planes that do not intersect

Parallel lines (ll)

- parallel lines are coplanar and do not intersect

Perpendicular lines (⊥)

- perpendicular lines intersect at 90 ° angles

Angle

Measure of an angle

Congruent Angles

Acute angle

The union of two noncollinear rays, line, or segments

The number of degrees between the 2 sides of an angle

Two angles are congruent iff they have the same measurement

An angle whose measure <90 degrees

Angle

The union of two noncollinear rays, line, or segments

Measure of an angle

The number of degrees between the 2 sides of an angle

Definition of midpoint

Definition of bisector

Midpoint Theorem

Segment Addition Postulate

If T is the midpoint of line segment CE, then CT = CE

If ray TP is the bisector of <RTE, then m<RTP = m<PTE

If T is the midpoint of line segment CE, then TE = 1/2 CE

CT + TE = CE

Definition of midpoint

If T is the midpoint of line segment CE, then CT = CE

Definition of bisector

If ray TP is the bisector of <RTE, then m<RTP = m<PTE

angle

vertex

What are the 4 ways to name an angle?

When can you not name an angle by it's…

- a figure made up of two rays, or sides, that have a common…

- the common endpoint where two rays meet

- the vertex ... - the vertex and a point on each side ... - use th…

- when the vertex point is the vertex for more than one angle…

angle

- a figure made up of two rays, or sides, that have a common…

vertex

- the common endpoint where two rays meet

3(n+5)=3n+15... ⁻(x−8)=⁻x+8

7x+y=9... y=3... then 7x+3=9

5x+12-2x=18... then 3x+12=18

3+x=3+x

distributive property

substitution property (replacing)

substitution property (simplifying, combining like terms)

reflexive property (order matters)

3(n+5)=3n+15... ⁻(x−8)=⁻x+8

distributive property

7x+y=9... y=3... then 7x+3=9

substitution property (replacing)

Complementary Angles

Supplementary angles

vertical angles

congruent angles

a pair of angles whose measures have a sum of 90°

a pair of angles whose measures have a sum of 180°

Opposite or non-adjacent angles formed by intersecting lines.…

angles that have the same measure

Complementary Angles

a pair of angles whose measures have a sum of 90°

Supplementary angles

a pair of angles whose measures have a sum of 180°

electron geometry for two regions

electron geometry for three regions

electron geometry for four regions

electron geometry for five regions

linear

trigonal planar

tetrahedral

trigonal bipyramidal

electron geometry for two regions

linear

electron geometry for three regions

trigonal planar

equiangular

acute triangle

acute angle

right triangle

is a triangle whose angles are all congruent

has three acute angles

is an angle whose measure is between 0 and 90

contains one right angle

equiangular

is a triangle whose angles are all congruent

acute triangle

has three acute angles

Point

Line

Ray

Segment

•a location in space ... •it has no size ... •name a ____ by a capi…

•a series of points that extend in two opposite directions ... •…

•a part of a line with one endpoint ... •name a ___ using two po…

•part of a line with two end points ... •name a ____ by its endp…

Point

•a location in space ... •it has no size ... •name a ____ by a capi…

Line

•a series of points that extend in two opposite directions ... •…

Right Angle

Obtuse Angle

Acute Angle

Straight Angle

An angle with a measure of 90

An angle with a measure greater than 90 but less than 180

An angle with a measure less than 90 but greater than 0

An angle with a measure of 180

Right Angle

An angle with a measure of 90

Obtuse Angle

An angle with a measure greater than 90 but less than 180

corresponding angles

supplementary angles

adjacent angles

complimentary angles

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

Two or more angles whose sum is 180 degrees

Angles that have a common side and a common vertex (corner po…

Two angles whose sum is 90 degrees

corresponding angles

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

supplementary angles

Two or more angles whose sum is 180 degrees

parallel lines

scale factor

alternate exterior angles

alternate interior angles

equidistant lines in the same plane that never intersect

the ratio of any two corresponding lengths in two similar geo…

outside angles that lie on opposite sides of the transversal

inside angles that lie on opposite sides of the transversal

parallel lines

equidistant lines in the same plane that never intersect

scale factor

the ratio of any two corresponding lengths in two similar geo…

Postulate

Theorem

Converse

Complementary Angles

A true statement that does not need to be proved.

A statement that can be proven

To switch the hypothesis and conclusion of a conditional stat…

Two angles whose measures equal 90 degrees

Postulate

A true statement that does not need to be proved.

Theorem

A statement that can be proven

Adjacent angles

Vertical angles

Complementary angles

Corresponding angles

Pair of angles with a common vertex and share a side

Angles opposite each other when two lines intersect

Two angles with a sum of 90 degrees

Angles that correspond to one another when lines cross

Adjacent angles

Pair of angles with a common vertex and share a side

Vertical angles

Angles opposite each other when two lines intersect

Adjacent angles

Vertical angles

Complementary angles

Corresponding angles

Pair of angles with a common vertex and share a side

Angles opposite each other when two lines intersect

Two angles with a sum of 90 degrees

Angles that correspond to one another when lines cross

Adjacent angles

Pair of angles with a common vertex and share a side

Vertical angles

Angles opposite each other when two lines intersect

Right Angle

Obtuse Angle

Acute Angle

Straight Angle

An angle with a measure of 90

An angle with a measure greater than 90 but less than 180

An angle with a measure less than 90 but greater than 0

An angle with a measure of 180

Right Angle

An angle with a measure of 90

Obtuse Angle

An angle with a measure greater than 90 but less than 180

parallel lines

scale factor

alternate exterior angles

alternate interior angles

equidistant lines in the same plane that never intersect

the ratio of any two corresponding lengths in two similar geo…

outside angles that lie on opposite sides of the transversal

inside angles that lie on opposite sides of the transversal

parallel lines

equidistant lines in the same plane that never intersect

scale factor

the ratio of any two corresponding lengths in two similar geo…

Corresponding Angles Postulate

Converse of Corresponding Angles Postu…

Alternate Interior Angles

Alternate Interior Angles Theorem

If two parallel lines are crossed by a transversal, then the…

If any two lines are crossed by a transversal and the corresp…

The pair of angles that are inside the two lines and on oppos…

If two parallel lines are crossed by a transversal, then each…

Corresponding Angles Postulate

If two parallel lines are crossed by a transversal, then the…

Converse of Corresponding Angles Postu…

If any two lines are crossed by a transversal and the corresp…

Right Angle

Obtuse Angle

Acute Angle

Straight Angle

An angle with a measure of 90

An angle with a measure greater than 90 but less than 180

An angle with a measure less than 90 but greater than 0

An angle with a measure of 180

Right Angle

An angle with a measure of 90

Obtuse Angle

An angle with a measure greater than 90 but less than 180

Parallel Lines

Skew Lines

Parallel Planes

If two parallel planes are cut by a th…

COPLANAR lines that do not intersect

NON coplanar lines that to not intersect (think left/right an…

Planes that do not intersect (Think floor and ceiling)

If planes X and Y are parallel, then their lines of intersect…

Parallel Lines

COPLANAR lines that do not intersect

Skew Lines

NON coplanar lines that to not intersect (think left/right an…