Postulates and Properties Flashcards
What are all of the Properties of Inequality?
If a > b and c ≥ d, then a + c > b + d
If a > b and c > 0, then ac > bc and a/c > b/c
If a > b and c < 0, then ac < bc and a/c < b/c
If a > b and b > c, then a > c
If a = b + c and c > 0, then a > b
What are all of the Properties of Proportion?
a/b = c/d is equivalent to:
ad = bc
a/c = b/d
b/a = d/c
(a+b)/b = (c+d)/d
a/b = c/d = e/f=…, then:
(a+c+e+…)/(b+d+f+…)= a/b =…
What is the Angle Addition Postulate? (in general and for straight angle?)
If point B lines is the interior of ∠AOC, then:
m∠AOB + m∠BOC = m∠AOC.
If ∠AOC is a straight angle and B is any point not on line AC, then m∠AOB + m∠BOC = 180.
Lines intersect at…
A point
Planes intersect at…
A line
What is the segment addition postulate?
When B is between A and C:
AB + BC = AC
What is the Corresponding Angles Postulate?
If two parallel lines are cut by a transversal, the corresponding angles are congruent.
What is the converse of the corresponding angles postulate?
If a transversal passes between two lines and the corresponding angles are congruent, then the lines are parallel
Lines contain at least __ points
2
planes contain at least __ noncollinear points
3
spaces contain at least __ noncoplanar points
4
through any 2 points there is…
exactly ONE line
through any 3 collinear points there is/are…
infinite planes
through any noncollinear points there is/are…
exactly ONE plane
if 2 points are in a plane, then…
the line containing those two points is also in the plane.
what is the ruler postulate?
- the points on a line can be paired with the real numbers in such a way that any two points can have coordination 0 and 1.
- once a coordinate system has been chosen in this way, the distance between any two points equals the absolute value of the difference of their coordinates
what is protractor postulate
on line AB in a given plane, choose any point O between A and B. Consider ray OA and ray OB and all rays that can be drawn from O on one side of line AB. These rays can be paired with the real numbers from O to 180 in such away that:
a. ray OA is paired iwht 0, and ray OB with 180
b. if ray OP is paired with x, and ray OQ with y, then measure of angle POQ = |x-y|
what is SSS postulate
if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent
what is SAS Postulate
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
what is ASA Postulate
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
What is AA Similarity Postulate
if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
what is arc addition postulate
the measure of the arc formed by two adjacent arcs is the sum of the measures of these two arcs
what is the area of a square
the area of a square is the square of the length of a side
what is area congruence postulate
if two figures are congruent, then they have the same area.
what is area addition postulate
the area of a region is the sum of the area of its non-overlapping parts
