Geometery Mid-Term Review
Terms
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- 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
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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. - 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. - 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. - 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
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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. - 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.