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Geometry Cheat Sheet: Postulates and Theorems, Cheat Sheet of Geometry

Cedarville UniversityGeometry

Postulates, theorems, properties and sample problems for the Geometry exam

Typology: Cheat Sheet

2019/2020

Uploaded on 10/09/2020

alfred67
alfred67 🇺🇸

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Geometry Cheat Sheet
Chapter 1
Postulate 1-6
Segment Addition Postulate - If three points A, B, and C are collinear and B is between A
and C, then AB + BC = AC.
Postulate 1-7
Angle Addition Postulate - If point B is in the interior of AOC, then
m AOB + m BOC = m AOC.
Adjacent Angles - two coplanar angles with a common side, a common vertex, and no
common interior points.
Vertical Angles - two angles whose sides are opposite rays.
Complementary Angles - two angles whose measures have a sum of 90. Each angle is
called the complement of the other.
Supplementary Angles - two angles whose measures have a sum of 180. Each angle is
called the supplement of the other.
Postulate 1-9 Linear Pair Postulates - If two angles form a linear pair, then they are
supplementary.
Angle Bisector - a ray that divides an angle into two congruent angles. Its endpoint is at
the angle vertex within the ray, a segment with the same endpoint is also an angle
bisector.
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Geometry Cheat Sheet

Chapter 1

 Postulate 1-

Segment Addition Postulate - If three points A, B, and C are collinear and B is between A

and C, then AB + BC = AC.

 Postulate 1-

Angle Addition Postulate - If point B is in the interior of AOC, then

m AOB + m BOC = m AOC.

 Adjacent Angles - two coplanar angles with a common side, a common vertex, and no

common interior points.

 Vertical Angles - two angles whose sides are opposite rays.

 Complementary Angles - two angles whose measures have a sum of 90. Each angle is

called the complement of the other.

 Supplementary Angles - two angles whose measures have a sum of 180. Each angle is

called the supplement of the other.

 Postulate 1-9 Linear Pair Postulates - If two angles form a linear pair, then they are

supplementary.

 Angle Bisector - a ray that divides an angle into two congruent angles. Its endpoint is at

the angle vertex within the ray, a segment with the same endpoint is also an angle

bisector.

Constructions

 Constructing Congruent Segments –

 Step One: Draw a ray with endpoint C.

 Step Two: Open the compass to the length of AB.

 Step Three: With the same compass setting, put the compass point on point C. Draw an

arc that intersects the ray. Label the point of intersection D.

 Constructing Congruent Angles –

 Step One: Draw a ray with endpoint S.

 Step Two: With the compass on vertex A, draw an arc that intersects the sides of A.

Label the points of intersection B and C.

 Step Three: With the same compass setting, put the compass point on point S. Draw an

arc and label its point of intersection with the ray as R.

 Step Four: Open the compass to the length BC. Keeping the same compass setting, put

the compass point on R. Draw an arc to locate point T.

 Step Five: Draw ST

 Constructing the Perpendicular Bisector –

 Step One: Put the compass on point A and draw a long arc. Be sure the opening is

greater than ½ AB.

 Step Two: With the same compass setting, put the compass point on point B and draw

another long arc. Label the points where the two arcs intersect as X and Y.

 Step Three: Draw XY. Label the point of intersection of AB and XY as M, the midpoint of

AB.

Negation of a statement p is the opposite of the statement.

The truth value of a conditional is either true or false.

Deductive Reasoning (Logical Reasoning) - the process of reasoning logically from given

statements or facts to a conclusion

 Same-Side Interior Angles Theorem  Corresponding Angles Postulate  Alternate Exterior Angles Theorem  Converse of the Alternate Interior Angles Theorem  Converse of the Same-Side Interior Angles Theorem  Converse of the Corresponding Angles Postulate  Converse of the Alternate Exterior Angles Theorem  Vertical Angles Theorem  Congruent Supplements Theorem  Congruent Complements Theorem Triangles :  Triangle-Sum Theorem  Triangle Exterior Angle Theorem  Third Angles Theorem  Side-Side-Side Postulate  Side-Angle-Side Postulate  Angle-Side-Angle Postulate  Angle-Angle-Side Postulate  Congruent Parts of Congruent Triangles are Congruent (CPCTC)  Hypotenuse Leg (HL) Theorem  SSS, SAS, ASA, AAS  Isosceles Triangle Theorem  Converse of the Isosceles Triangle Theorem  Triangle Midsegment Theorem  Perpendicular Bisector Theorem  Converse of the Perpendicular Bisector Theorem  Angle Bisector Theorem  Converse of the Angle Bisector Theorem  Concurrency of Perpendicular Bisector Theorem  Concurrency of Angle Bisector Theorem  Concurrency of Medians Theorem  Concurrency of Altitudes Theorem Inequalities  Comparison Property of Inequality  Corollary to the Triangle Exterior Angle Theorem

 Theorem 5-  Theorem 5-  Theorem 5-12 (Triangle Inequality Theorem)  Hinge Theorem  Converse of the Hinge Theorem