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43 Cards in this Set

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  • 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 a-c=b-c.
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
[Side-Side-Side]
If three sides of one triangle are equal to the same of another, those triangles are congruent.
SAS Theorem
[Side-Angle-Side]
If two sides and their included side of one triangle equal to the same in another, those triangles are congruent.
ASA Theorem
[Angle-Side-Angle]
If two angles and their included side of one triangle are equal to the same in another, those triangles are congruent.
AAS Theorem
[Angle-Angle-Side]
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
[Leg-Leg]
LA
[Leg-Acute Angle]
HA
[Hypotenuse-Acute Angle]
HL
[Hypotenuse-Leg]
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.