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43 Cards in this Set
 Front
 Back
Segment Addition Theorem

If Q is between P and R, the PQ+QR=PR.


Angle Addition Theorem

If R is in the interior of <PQS, then <PQR+<RQS=<PQS.


Addition Property

If a=b, then a+c=b+c.


Subtraction Property

If a=b, then ac=bc.


Multiplication Property

If a=b, then ac=bc.


Division Property

If a=b, then a/c=b/c.


Distributive Property

If a(b+c), then ab+ac.


Substitution Property

If a=b, then a can be replaced by b (or vice versa).


Reflexive Property

a=a


Symmetric Property

If a=b, then b=a.


Transitive Property

If a=b and b=c, then a=c.


Supplement Theorem

If two angles form a linear pair, then they are supplementary angles.


Supplement Angle Theorem

Angles supplementary to the same angle are congruent.


Complement Angle Theorem

Angles complementary to the same angle are congruent.


Congruent Angle Theorem

Congruence of angles is reflexive, symmetric, and transitive.


Vertical Angle Theorem

Vertical angles are congruent.


Right Angle Theorem

All right angles are congruent.


Perpendicular Line Theorem

Perpendicular lines intersect to form four right angles.


Alternate Interior Theorem

If two parallel lines are intersected by a transversal, then their alternate interior angles are congruent.


Alternate Exterior Theorem

If two parallel lines are intersected by a transversal, then their alternate exterior angles are congruent.


Corresponding Angle Theorem

If two parallel lines are intersected by a transversal, then their corresponding angles are congruent.


Consecutive Interior Theorem

If two parallel lines are intersected by a transversal, then their consecutive interior angles are supplementary.


Perpendicular Transversal Theorem

If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other as well.


Angle Sum Theorem

The three angles inside of a triangle have a sum of 180 degrees.


Third Angle Theorem

If two angles of one triangle are equal to two angles of another triangle, then their third angles must also be equal.


Exterior Angle Theorem

The measure of an exterior angle for a triangle is equal to the sum of its two remote interior angles.


CPCTC Theorem

[This stands for "Corresponding Parts of Congruent Triangles are Congruent."]
If two triangles are congruent, then all of their corresponding parts (angles and sides) are also congruent...and vice versa. 

SSS Theorem

[SideSideSide]
If three sides of one triangle are equal to the same of another, those triangles are congruent. 

SAS Theorem

[SideAngleSide]
If two sides and their included side of one triangle equal to the same in another, those triangles are congruent. 

ASA Theorem

[AngleSideAngle]
If two angles and their included side of one triangle are equal to the same in another, those triangles are congruent. 

AAS Theorem

[AngleAngleSide]
If two angles and a nonincluded side of one triangle are equal to the same in another, those triangles are congruent. 

AAA & ASS

note: There are no theorems for the 'car company' or the 'bad butt' word.


Isosceles Triangle Theorem

If two sides of a triangle are congruent, then the angles opposite those sides are also congruent (or vice versa).


Equilateral Triangle Theorem

If a triangle is equilateral, then it is also equiangular and each angle measures 60 degrees.


Right Angle Shortcut Theorems

If the _ and _ of one right triangle are equal to the same in another, then these triangles are congruent.


LL

[LegLeg]


LA

[LegAcute Angle]


HA

[HypotenuseAcute Angle]


HL

[HypotenuseLeg]


Longer Side Theorem

If one side of a triangle is longer then another, then the angle opposite the longer side is greater than the angle opposite the lesser side.


Greater Angle Theorem

If one angle of a triangle is greater then another, then the side opposite the greater angle is longer than the one opposite the smaller angle.


Exterior Angle Inequality Theorem

An exterior angle of a triangle has a measure greater than either of its remote interior angles.


Triangle Side Inequality Theorem

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
