Download B1 Regents – Prove Basic Geometry Theorems by Direct Proofs

B1 Regents – Prove Basic Geometry Theorems by Direct Proofs
Angle Postulates & Theorems:
Angle Addition Postulate
If P is the interior of RST, then mRSP + mPST = mRST.
Angle Measure: Properties of Equality & Congruence
Reflexive: For any angle A, mA = mA.
Symmetric: If mA = mB, then mB = mA.
Transitive: If mA = mB, and mB = mC, then mA = mC.
Right Angle Congruence Theorem
All right angles are congruent.
Congruent Supplements Theorem
If two angles are supplementary to the same angle (or to congruent angles) then they are congruent.
If m1 + m2 = 180° and m2 + m3 = 180°, then 1
3.
Congruent Complements Theorem
If two angles are complementary to the same angle (or to congruent angles) then the two angles are congruent.
If m4 + m5 = 90° and m5 + m6 = 90°, then 4
6.
Linear Pair Postulate
If two angles form a linear pair, then they are supplementary.
Vertical Angles Theorem
Vertical angles are congruent.
Line Segment Postulates & Theorems:
Point, Line & Plane Postulates:
 Through any two points there exists exactly one line.
 A line contains at least two points.
 If two lines intersect, then their intersection is exactly one point.
 Through any three non collinear points there exists exactly one plane.
 A plane contains at least three non collinear points.
 If two points lie in a plane, then the line containing them lies in the plane.
 If two planes intersect, then their intersection is a line.
Segment Length: Properties of Equality & Congruence
Reflexive: For any segment AB, AB = AB.
Symmetric: If AB = CD, then CD = AB.
Transitive: If AB = CD and CD = EF, then AB = EF.
Parallel Postulate
If there is a line and a point not on the line,
then there is exactly one line
through the point parallel to the
given line.
Perpendicular Postulate
If there is a line and a point not on the line,
then there is exactly one line through
the point perpendicular to the given line.
Theorems about Perpendicular Lines
 If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.
 If two sides of two adjacent acute angles are perpendicular, then the angles are complementary.
 If two lines are perpendicular, then they intersect to form four right angles.
Proving Lines Are PARALLEL
Corresponding Angles Converse
If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.
Alternate Interior Angles Converse
If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are
parallel.
Consecutive Interior Angles Converse
If two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines
are parallel.
Alternate Exterior Angles Converse
If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are
parallel.
Theorems about parallel & perpendicular lines
If two lines are parallel to the same line, then they are parallel to each other.
In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.