Proof Postilates and Properties and vocab Flashcards
Commutative property of addition
a+b=b+a
Commutative property of multiplication
ab=ba
Associative property of addition
(a+b)+c=a+(b+c)
Associative property of multiplication
(ab)c=a(bc)
Distributive property
A(b+c)=ab+ac
Reflective property
a=a
Transitive property
a=b b=c
Addition property of equity
a=b a+c =b+c
Symmetric property
a=b b=a
Subtraction property of equity
a=b a-c=b-c
Multiplication property of equality
a=b ac=bc
Division property of equity
a=b a/c b/c provided c dowse not = 0 also If a=b and b=c then a/c=b/d provided that c or d does not = 0
Square root property
A^2 = b then a=+-b square rooted
Zero product property
ab= 0 then a=0 and/or b0
AIA
When two lines are crossed by another line (which is called the Transversal), the pairs of angles. • on opposite sides of the transversal. • but inside the two lines. are called Alternate Interior Angles.
Altitude
An altitude of a triangle. An altitude is a line which passes through a vertex of a triangle, and meets the opposite side at right angles. A triangle has three altitudes. … The length of a perpendicular from a side of the triangle to the opposite vertex.
Angle bisector
An altitude of a triangle. An altitude is a line which passes through a vertex of a triangle, and meets the opposite side at right angles. A triangle has three altitudes. … The length of a perpendicular from a side of the triangle to the opposite vertex.
Congruence
In elementary geometry the word congruent is often used as follows. The word equal is often used in place of congruent for these objects. Two line segments are congruent if they have the same length. Two angles are congruent if they have the same measure.
C.A.
When two lines are crossed by another line (which is called the Transversal), the angles in matching corners are called corresponding angles. When the two lines are parallel Corresponding Angles are equal.
Iscosolise triangle
A triangle with two congruent sides and both base angles congruent
Linear pair
Definition. A linear pair is a pair of adjacent, supplementary angles. Adjacent means next to each other, and supplementary means that the measures of the two angles add up to equal 180 degrees.
Midpoint
Midpoint of a line segment. Definition: A point on a line segment that divides it into two equal parts. The halfway point of a line segment.
Parollelagram
a four-sided plane rectilinear figure with opposite sides parallel.
Perpendicular
In elementary geometry, the property of being perpendicular (perpendicularity) is the relationship between two lines which meet at a right angle (90 degrees). The property extends to other related geometric objects. A line is said to be perpendicular to another line if the two lines intersect at a right angle.
Right angle
An angle that measures 90 degrees
Segment bisector
Segment Bisector: A point, segment, line, or plane that divides a line segment into two equal parts. The bisector of a segment always contains the midpoint of the segment
Supplementary angles
Angles that add up to 180
Vertical angles
Vertical Angles. Vertical angles are a pair of non-adjacent angles formed when two lines intersect. We see intersecting lines all the time in our real world. Here, we see two vapor trails that intersect.
Line postulate
Through 2 points there can only be 1 line
Line intersection postulate
There is 1 point of intersection between two lines
Segment duplication postulate
You can construct a segment congruent to another segment
Angle duplication postulate
You can create a congruent angle
Midpoint postulate
You can have 1 midpoint o a segment
Angle bisector postulate
You can construct 1 angle bisector through 1 angle
Parallel postulate
Through a point not on a given line you can construct 1 parallel line
Perpendicular postulate
Through a point you can construct 1 perpendicular
Segment addition postulate
If b is on ac then ab+by=ac
Angle addition postulate
Angle a + angle b =angle c if angle b cuts angle c
Linear pair postulate
If two angles are a linier pair then they are supplementary.
Corresponding angles postulate
If two parallel lines are cut by a transversal then the corresponding angles are congruent
SSS congruence postulate
If three sides of 1 triangle are congruent to another triangles side then the triangle is congruent
SAS
S angle side is congruent
A side angle
Is congruent
Cpctc
Corespondent part of congruent triangles are congruent
