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Level 136

Theorems & Properties for Angles & Lines


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Vertical Angles
Angles opposite one another when two lines intersect.
angles formed by parallel lines cut by a transversal #1
if 2 parallel lines are cut by a transversal, then the alternate interior angles formed are congruent
angles formed by parallel lines cut by a transversal #2
if 2 parallel lines are cut by a transversal, then the alternate exterior angles formed are congruent
angles formed by parallel lines cut by a transversal #3
if 2 parallel lines are cut by a transversal, then the corresponding angles formed are congruent
supplementary angles #1
supplementary angles from a straight line
supplementary angles #2
if 2 angles are congruent, then they're supplements are congruent
complementary angles #1
complementary angles form a right angle
complementary angles #2
if 2 angles are congruent, the they're complements are congruent
Perpendicular lines
lines in a plane that intersect to form 4 right angles
Right Angles
if 2 angles are right angles, then they're congruent
Midpoint
if a line segment has a midpoint, then the 2 segments formed are congruent
half segments
halves of congruent segments are congruent
half angles
halves of congruent angles are congruent
Bisector
if a line bisects a line segment, then it intersects it at its midpoint
bisector (converse)
if a line intersects a segment at its midpoint, then it bisected it
Perpendicular Bisector
if a line perpendicularly bisects a line segment, then it intersects it at its midpoint and forms right angles
Angle Bisector
if a line bisects an angle, then the 2 angles formed are congruent
Reflexive Property
a segment (or angle) is congruent to itself
Symmetric Property
when two segments or two angles are congruent, you can flip them over and they will still be congruent
Transitive Property
if two segments or two angles are congruent to the same segment of angle, they are congruent to each other
addition postulate
if congruent segments are added to other congruent segments, then the sums are congruent// if congruent angles are added to other congruent angles, then the sums are congruent
subtraction postulate
if congruent segments are subtracted from other congruent segments, then the differences are congruent// of congruent angles are subtracted from other congruent angles, then the differences are congruent
substitution postulate
a quantity may be substituted for its equal in any expression **ALWAYS USED TO GET THE ANSWER TO AN ADDITION/SUBTRACTION PROBLEM IN A PROOF**