Download Definitions, Postulates, Theorems, and Corollaries First Semester

Definitions, Postulates, Theorems, and Corollaries
First Semester
Geometry
Chapter 1
1.
Equidistant
2.
Point
3.
Line
4.
Plane
5.
Space
6.
Collinear
7.
Non-collinear
8.
Coplanar
9.
Non-coplanar
10.
Intersect
11.
Intersection
12.
Segment
13.
Ray
14.
Opposite rays
15.
Coordinate of a point
16.
Length of a segment
17.
Postulate
18.
Ruler Postulate (Postulate 1)
19.
Segment Addition Postulate (Postulate
2)
20.
Congruent (≅)
21.
Congruent (≅) segments
Chapter 2
1.
If-then statements ⇒ conditional
statements
2.
Hypothesis
3.
Conclusion
4.
Converse
5.
Counterexample
6.
If and only if statements ⇒
biconditional statements
7.
Addition Property of equality
8.
Subtraction Property of equality
9.
Multiplication Property of equality
10.
Division Property of equality
11.
Substitution of equality
12.
Reflexive of equality
13.
Symmetric of equality
14.
Transitive of equality
15.
Reflexive Property of congruence
16.
Symmetric Property of congruence
17.
Transitive Property of congruence
18.
Distributive
Chapter 3
1.
Intersecting lines
2.
Non-Intersecting lines
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
Midpoint of a segment (Midpt)
Bisector of a segment
Angle
Sides
Vertex
Acute angle
Right angle
Obtuse angle
Straight angle
Angle Addition Postulate (Postulate 4)
– 2 Parts
Congruent angles
Adjacent angles
Angle bisector
Postulate 5
Postulate 6
Postulate 7
Postulate 8
Postulate 9
Theorem 1-1
Theorem 1-2
Theorem 1-3
Theorem 2-1 : Midpoint Theorem
Theorem 2-2 : Angle Bisector
Theorem
Reasons We Can Use in a Proof:
a. Given Information
b. Definitions
c. Postulates (including algebra
properties)
d. Proven theorems
e. Corollaries
Complementary angles (complements)
Supplementary angles (supplements)
Vertical angles
Theorem 2-3
Perpendicular Lines ( ⊥ )
Theorem 2-4
Theorem 2-5
Theorem 2-6
Theorem 2-7
Theorem 2-8
3.
Parallel lines (
4.
Skew lines
)
First Semester Postulates, Theorems, Corollaries and Definition – Page 1
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
Parallel planes
Definition of a line parallel to a plane
Theorem 3-1
Transversal
Alternate interior angles (alt. int)
Alternate exterior angles (alt. ext)
Same-Side Interior (s-s int)
Same-side Exterior (s-s ext)
Corresponding (corr.)
Postulate 10
Theorem 3-2
Theorem 3-3
Theorem 3-4
Postulate 11
Theorem 3-5
Theorem 3-6
Theorem 3-7
Theorem 3-8
Theorem 3-9
Theorem 3-10
Auxiliary Lines
Triangle
Vertex (vertices)
Sides of a ∆
Scalene Triangle
Isosceles Triangle
Equilateral Triangle
Equiangular Triangle
Chapter 4
1.
Congruent Polygons
2.
CPCTC
3.
Regular polygons
4.
Common Side
5.
Postulate 12 – SSS Post
6.
Postulate 13 – SAS Post
7.
Postulate 14 – ASA Post
8.
Theorem 4-3 – AAS
9.
Definition of a Line perpendicular to
a plane
10.
Isosceles Triangle
11.
Legs of an Isosceles Triangle
12.
Base of an Isosceles Triangle
13.
Base Angles of an Isosceles Triangle
14.
Vertex angle of an Isosceles Triangle
15.
Theorem 4-1 – Isosceles Triangle
Theorem
16.
Corollary 1 to Theorem 4-1
17.
Corollary 2 to Theorem 4-1
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
Acute Triangle
Obtuse Triangle
Right Triangle
Theorem 3-11
Corollary 1 to Theorem 3-11
Corollary 2 to Theorem 3-11
Corollary 3 to Theorem 3-11
Corollary 4 to Theorem 3-11
Exterior angles of a triangle
Remote interior angles of a triangle
Theorem 3-12
Polygon
Convex polygon
Concave polygon
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Diagonals of a polygon
Theorem 3-13
Theorem 3-14
Equiangular Polygon
Equilateral Polygon
Regular polygon
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
Corollary 3 to Theorem 4-1
Theorem 4-2
Corollary to Theorem 4-2
Overlapping Triangles
Right Triangle
Hypotenuse
Theorem 4-4 – HL Theorem
LL Theorem
HA Theorem
LA Theorem
Median of a Triangle
Altitude of a Triangle
Perpendicular Bisector
Theorem 4-5
Theorem 4-6
Definition of the Distance from a
point to a line
Theorem 4-7
Theorem 4-8
34.
35.
First Semester Postulates, Theorems, Corollaries and Definition – Page 2