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Proofs: Theorems and Postulates
Theorems and postulates used in geometric proofs.
16
Mathematics
10th Grade
11/09/2010

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Cards

Term
AAS Theorem
Definition
If two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.
Term
HL Theorem
Definition
If the hypotenuse and a leg of one right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent.
Term
Theorem 4-2
Definition
If two angles of a triangle are congruent, then the sides opposite those angles are congruent.
Term

Theorem 4-1

The Isosceles Triangle Theorem

Definition
If two sides of a triangle are congruent, then the sides opposite those sides are congruent.
Term
SSS Postulate
Definition
If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
Term
SAS Postulate
Definition
If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
Term
ASA Postulate
Definition

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

Term

Postulate 10

Proving Lines Parallel

Definition
If two parallel lines are cut by a transversal, then corresponding angles are congruent.
Term
Postulate 11
Definition
If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel.
Term
Theorem 2-7
Definition
If two angles are supplements of congruent angles (or of the same angle), then the two angles are congruent.
Term
Theorem 2-4
Definition
If two lines are perpendicular, then they form congruent adjacent angles.
Term
Theorem 2-5
Definition
If two lines form congruent adjacent angles, then the lines are perpendicular.
Term
Theorem 2-3
Definition
Vertical angles are congruent.
Term

Theorem 2-2

Angle Bisector Theorem

Definition
If BX is the bisector of <ABC, then m<ABX = 1/2 <ABC and m<XBC = 1/2m <ABC. 
Term
Addition Property
Definition
If a=b and c=d, then a+c = b+d.
Term
Subtraction Property
Definition
If a=b and c=d, then a-c = b-d.
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