Download Geometry Semester 1 Final Proof Word Bank

Geometry Semester 1 Final Proof Word Bank
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*****For “GIVEN” right the letter G
Postulates
1.
3.
5.
7.
9.
11.
13.
15.
17.
19.
21.
23.
25.
27.
29.
Ruler Postulate
Segment Addition Postulate
Protractor Postulate
Angle Addition Postulate
Through any two points there exists exactly one line
A line contains at least two points.
If two lines intersect, then their intersection is exactly one point.
Through any three noncollinear points there exists exactly one plane.
A plane contains at least three noncollinear points
If two points lie in a plane, then the line containing them lies in the plane.
If two planes interest, then their intersection is a line.
Linear Pair Postulate
Parallel Postulate
Perpendicular Postulate
Corresponding Angles Postulate
Theorems Continued
2.
4.
6.
8.
10.
12.
14.
16.
18.
20.
22.
24.
26.
28.
30.
31.
32.
34.
36.
38.
40.
42.
44.
46.
Corresponding Angle Converse
Slopes of Parallel Lines
Slopes of Perpendicular Lines
SSS Congruence Postulate
SAS Congruence Postulate
ASA Congruence Postulate
Area of a Square Postulate
Area Addition Postulate
Definitions
33.
35.
37.
39.
41.
43.
45.
47.
48.
* Note- Only the most commonly used definitions for proofs are listed below.
49. Definition of Midpoint
50.
51.
Definition of Angle Bisector
52.
53.
Definition of Segment Bisector
54.
55.
Definition of Vertical Angles
56.
57.
Definition of Linear Pair
58.
59.
61.
63.
65.
67.
Definition of Complementary Angles
Definition of Complements
Definition of Supplementary Angles
Definition of Supplements
Definition of Perpendicular Lines
60.
62.
64.
66.
68.
69.
71.
73.
75.
Definition of Transversal
Definition of Segment Bisector
Definition of Angle Bisector
Definition of Congruent Triangles
78.
80.
82.
84.
86.
88.
90.
92.
94.
96.
98.
Reflexive Property of Segment Congruence
Symmetric Property of Segment Congruence
Transitive Property of Segment Congruence
Reflexive Properties of Angle Congruence
Symmetric Properties of Angle Congruence
Transitive Properties of Angle Congruence
Right Angle Congruence Thm
Congruent Supplements Thm
Congruent Complements Thm
Vertical Angles Thm
If two lines intersect to form a linear pair of congruent angles, then the lines are
perpendicular.
If two sides of two adjacent acute angles are perpendicular, then the angles are
complementary.
If two lines are perpendicular, then they intersect to form four right angles.
Alternate Interior Angles Thm
Consecutive Interior Angles Thm
70.
72.
74.
76.
77.
79.
81.
83.
85.
87.
89.
91.
93.
95.
97.
99.
Theorems
100.
102.
104.
106.
108. Acute angles of a right triangle are complementary
110. Exterior Angle Thm
111. Third Angles Thm
112.
114.
116.
118.
120.
Reflexive Property of Congruent Triangles
Symmetric Property of Congruent Triangles
Transitive Property of Congruent Triangles
AAS Congruence Theorem
Converse of the Angle Bisector Thm
Base Angles Thm
If a triangle is equilateral, then it is equiangular.
Converse of the Base Angles Theorem
If a triangle is equiangular, then it is equilateral
Hypotenuse-Leg (HL) Congruence Thm
Perpendicular Bisector Thm
Converse of the Perpendicular Bisector Thm
Angle Bisector Thm
CPCTC- Corresponding Part of Congruent Triangles are congruent
Concurrency of Perpendicular Bisectors of a Triangle Thm
Concurrency of Angle Bisectors of a Triangle Thm
Concurrency of Medians of a Triangle Thm
Concurrency of Altitudes of a Triangle Thm
Midsegment Thm
If one side of a triangle is longer than another side, then the angle opposite the
longer side is larger than the angle opposite the shorter side.
If one angle of a triangle is larger than another angle, then the side opposite the
larger angle is longer than the side opposite the smaller angle.
Exterior Angle Inequality Thm
Triangle Inequality Thm
Hinge Thm
Converse of the Hinge Thm
Interior Angles of a Quadrilateral Thm
If a quadrilateral is a parallelogram, then its opposite sides are congruent.
If a quadrilateral is a parallelogram, then its opposite angles are congruent.
If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.
If a quadrilateral is a parallelogram, then its diagonals bisect each other.
If both pairs of opposite sides of a quadrilateral are congruent, then the
quadrilateral is a parallelogram.
If both pairs of opposite angles of a quadrilateral are congruent, then the
quadrilateral is a parallelogram.
If an angle of a quadrilateral is supplementary to both of its consecutive angles,
then the quadrilateral is a parallelogram.
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a
parallelogram.
If one pair of opposite sides of a quadrilateral are congruent and parallel, then the
quadrilateral is a parallelogram.
A quadrilateral is a rhombus if and only if (iff) it has four congruent sides.
A quadrilateral is a rectangle if and only if (iff) it has four right angles
A quadrilateral is a square if and only if (iff) it is a rhombus and a rectangle.
A parallelogram is a rhombus iff its diagonals are perpendicular.
A parallelogram is a rhombus iff its each diagonal bisects a pair of opposite
angles.
A parallelogram is a rectangle iff its diagonals are congruent.
If a trapezoid is isosceles, then each pair of base angles is congruent.
If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid.
A trapezoid is isosceles iff its diagonals are congruent.
Midsegment Theorem for Trapezoids
If a quadrilateral is a kite, then its diagonals are perpendicular.
If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.
Area of A Rectangle Thm
Area of a Parallelogram Thm
Area of a Triangle Thm
Area of a Trapezoid Thm
Area of a Kite Thm
Area of a Rhombus Thm
Alternate Exterior Angles Thm
Perpendicular Transversal Thm
Alternate Interior Angles Converse
101. Consecutive Interior Angles Converse
103. Alternate Exterior Angles Converse
105. If two lines are parallel to the same line, then they are parallel to each other.
107. In a plane, if two lines are perpendicular to the same line, then they are parallel to
each other.
109. Triangle Sum Thm
Properties of Equality ( Use these for values, segment measures, and
angle measures)
113.
115.
117.
119.
121.
122.
123.
124.
Addition Property of Equality
Subtraction Property of Equality
Multiplication Property of Equality
Division Property of Equality
Reflexive Property of Equality
Symmetric Property of Equality
Transitive Property of Equality
Substitution Property of Equality