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43 Cards in this Set
- Front
- Back
Segment Addition Theorem
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If Q is between P and R, the PQ+QR=PR.
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Angle Addition Theorem
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If R is in the interior of <PQS, then <PQR+<RQS=<PQS.
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Addition Property
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If a=b, then a+c=b+c.
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Subtraction Property
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If a=b, then a-c=b-c.
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Multiplication Property
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If a=b, then ac=bc.
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Division Property
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If a=b, then a/c=b/c.
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Distributive Property
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If a(b+c), then ab+ac.
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Substitution Property
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If a=b, then a can be replaced by b (or vice versa).
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Reflexive Property
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a=a
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Symmetric Property
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If a=b, then b=a.
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Transitive Property
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If a=b and b=c, then a=c.
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Supplement Theorem
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If two angles form a linear pair, then they are supplementary angles.
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Supplement Angle Theorem
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Angles supplementary to the same angle are congruent.
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Complement Angle Theorem
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Angles complementary to the same angle are congruent.
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Congruent Angle Theorem
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Congruence of angles is reflexive, symmetric, and transitive.
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Vertical Angle Theorem
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Vertical angles are congruent.
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Right Angle Theorem
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All right angles are congruent.
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Perpendicular Line Theorem
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Perpendicular lines intersect to form four right angles.
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Alternate Interior Theorem
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If two parallel lines are intersected by a transversal, then their alternate interior angles are congruent.
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Alternate Exterior Theorem
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If two parallel lines are intersected by a transversal, then their alternate exterior angles are congruent.
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Corresponding Angle Theorem
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If two parallel lines are intersected by a transversal, then their corresponding angles are congruent.
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Consecutive Interior Theorem
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If two parallel lines are intersected by a transversal, then their consecutive interior angles are supplementary.
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Perpendicular Transversal Theorem
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If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other as well.
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Angle Sum Theorem
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The three angles inside of a triangle have a sum of 180 degrees.
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Third Angle Theorem
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If two angles of one triangle are equal to two angles of another triangle, then their third angles must also be equal.
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Exterior Angle Theorem
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The measure of an exterior angle for a triangle is equal to the sum of its two remote interior angles.
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CPCTC Theorem
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[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. |
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SSS Theorem
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[Side-Side-Side]
If three sides of one triangle are equal to the same of another, those triangles are congruent. |
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SAS Theorem
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[Side-Angle-Side]
If two sides and their included side of one triangle equal to the same in another, those triangles are congruent. |
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ASA Theorem
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[Angle-Side-Angle]
If two angles and their included side of one triangle are equal to the same in another, those triangles are congruent. |
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AAS Theorem
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[Angle-Angle-Side]
If two angles and a nonincluded side of one triangle are equal to the same in another, those triangles are congruent. |
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AAA & ASS
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note: There are no theorems for the 'car company' or the 'bad butt' word.
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Isosceles Triangle Theorem
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If two sides of a triangle are congruent, then the angles opposite those sides are also congruent (or vice versa).
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Equilateral Triangle Theorem
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If a triangle is equilateral, then it is also equiangular and each angle measures 60 degrees.
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Right Angle Shortcut Theorems
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If the _ and _ of one right triangle are equal to the same in another, then these triangles are congruent.
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LL
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[Leg-Leg]
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LA
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[Leg-Acute Angle]
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HA
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[Hypotenuse-Acute Angle]
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HL
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[Hypotenuse-Leg]
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Longer Side Theorem
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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.
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Greater Angle Theorem
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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.
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Exterior Angle Inequality Theorem
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An exterior angle of a triangle has a measure greater than either of its remote interior angles.
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Triangle Side Inequality Theorem
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The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
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