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Level 165

Geometric Proofs II


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Congruent
A plane figure with the same size and shape.
common
Vertical Angles have no _____________________________ rays.
adjacent, supplementary
Linear pairs are two _______________ angles that are also ______________________.
Bisector
if a line bisects a line segment, then it intersects it at its midpoint
Addition Property of Equality
For all real numbers x, y, and z, if x = y, then x + z = y + z.
If a=b, then a-c=b-c
Subtraction Property of Equality
Substitution Property of Equality
For all real numbers x and y, if x = y , then y can be substituted for x in any expression and vice versa.
Multiplication Property of Equality
For all real numbers x, y, and z, if x = y, then xz = yz.
Division Property of Equality
For all real numbers x, y, and z, if x = y, and z ≠ 0, then x/z = y/z. You can divide each side of an equation by the same non-zero number and not change its truth value.
one
MULTIPLICATIVE IDENTITY
Line
A straight path that goes without end in two directions.
True
True or False? Through any three noncollinear points there is exactly one plane.
coordinate
The number that corresponds to a point on a number line
Midpoint
if a line segment has a midpoint, then the 2 segments formed are congruent
90
A right angle equals _________ degrees.
Vertical angles theorem
If two angles are vertical angles, then they are congruent.
Angle 1 and Angle 2
If angle 1 and angle 3 are supplements and angle 2 and angle 3 are supplements, then angle __ and angle __ are congruent due to the Congruent Supplements Theorem.
Congruent supplements theorem
if two angles are supplementary to the same angle (or to congruent angles), then they are congruent
Reflexive Property
Anything equals itself; a shared piece.
Symmetric Property
when two segments or two angles are congruent, you can flip them over and they will still be congruent
Transitive Property
if two segments or two angles are congruent to the same segment of angle, they are congruent to each other
addition postulate
if congruent segments are added to other congruent segments, then the sums are congruent// if congruent angles are added to other congruent angles, then the sums are congruent
subtraction postulate
if congruent segments are subtracted from other congruent segments, then the differences are congruent// of congruent angles are subtracted from other congruent angles, then the differences are congruent
Side-Side-Side (SSS)
If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
Partition Postulate
The whole is equal to the sum of its parts.
Right Angles
if 2 angles are right angles, then they're congruent
Linear pair
A pair of adjacent angles whose non-common sides are opposite rays.
Vertical Angles
Angles opposite one another when two lines intersect.
Subtraction Property of Equality
For all real numbers x, y, and z, if x = y, then x - z = y - z.
a/c = b/c
division property of equality
<b~= <b
reflexive property of congruence
Symmetric Property of Congruence
If line AB is congruent to line CD, then line CD is congruent to line AB.
transitive property of congruence
If line AB is congruent to line CD and line CD is congruent to line EF, then line AB is congruent to line EF.
Definition of complementary
angles that add up to 90
Definition of supplementary
angles that add up to 180
--abc~=---bcd
Definition of congruent segments
<ab~=<bc
Definition of congruent angles
A-------B---------C
Definition of segment bisector
A C
Definition of angle bisector
i
All right angles are congruent
Congruent Complements Theorem
if two angles are complementary to the same angle (or to congruent angles), then they are congruent
PT=2(OT)
midpoint theorem
Common Segments Theorem
Given collinear points A, B, C, and D arranged as shown, if segment AB is congruent to segment CD, then segment AC is congruent to segment BD.
Congruent supplementary angles are right angles
angles that add up to 90
Corresponding angles postulate and the converse
an angle that is located outside and an angle that is located inside that is directly under the first one
Alternate interior angles theorem and the converse
angles that are located inside that are opposite of each other
Alternate exterior angles theorem and the converse
angles that are located outside that are opposite of each other
same side interior theorem and the converse
Angles that are located inside that are on the same line
Parallel Postulate
if there is a line and a point not on the line then there is exactly one line through the point parallel to the given line
If <1 and <2 equivalent and adjacent then A is perpendicular to B
If two lines intersect to form congruent adjacent angles, then the lines are perpendicular
perp to one perp to the angle
If a transversal is perpendicular to one of two parallel lines, then its perpendicular to the other
If two lines are perpendicular to the same lines, then they are parallel
If A is perpendicular to C and B is perpendicular to C then A is parallel to B