Rules for Angle and Segment Proofs Flashcards
What is the addition property of equality?
If a = b, then a+b = b+c.
What is the subtraction property of equality?
If a=b, then a-c = b-c.
What is the multiplication property of equality?
If a = b, then ac = bc.
What is the division property of equality?
If a = b, then a/c = b/c.
What is the distributive property?
If a(b+c), then a(b+c) = ab + ac.
What is the substitution property?
If a = b, then “a” may be replaced by “b” in any expression or equation.
What is the reflexive property?
For any real number a = a.
What is the symmetric property?
If a = b, then b = a.
What is the transitive property?
If a = b, and b = c, then a = c.
What is the reflexive property of congruence?
For any segment AB, AB is congruent to AB.
What is the symmetric property of congruence?
If segment AB is congruent to segment CD, then segment CD is congruent to segment AB.
What is the transitive property of congruence?
If segment AB is congruent to segment CD, and segment CD is congruent to segment EF, then segment AB is congruent to segment EF.
What is the definition of congruence?
Segments
Segments are congruent if and only if they have the same measure:
If segment AB is congruent to segment CD, the AB = CD.
If AB = CD, then segment AB is congruent to segment CD.
What is the definition of a midpoint?
The midpoint of a segment divides the segment into two equal (congruent) parts:
If M is the midpoint of AB, then AM = MB.
What is the segment addition postulate?
If A, B, and C are collinear points and B is between A and C:
then segment AB + segment BC = segment AC.
What is the definition of congruence?
angles
The measure of angle A = the measure of angle B is the same as angle A is congruent to angle B.
What is the definition of an angles bisector?
An angle bisector divides an angle into two equal parts.
What is the definition of complementary angles?
Sum is 90 degrees or it is complementary.
What is the definition of supplementary angles?
Sum is 180 degrees or it is supplementary.
What is the definition of perpendicular?
Perpendicular lines form right angles.
What is the definition of a right angle?
A right angle = 90 degrees.
What is the definition of angle addition postulates?
The measure of angle ABC + the measure of angle DBC = angle ABC.
What is the vertical angles theorem?
If two angles are vertical, then they are congruent.
What is the complement theorem?
If two angles form a right angle, then they are complementary:
Right Angle implies Complementary.
What is the supplement theorem?
If two angles form a linear pair, then they are supplementary:
Linear Pair implies Supplementary.
What is the congruent complements theorem?
If angle A is complementary to angle B, and angle B is complementary to angle C, then angle A is congruent with angle C.
What is the congruent supplements theorem?
If angle A is supplementary to angle B, and angle B is supplementary to angle C, then angle A is congruent with angle C.
