![]() ![]() ![]() Measure of angle BAX is congruent to measure of angle CAX Complementary Angles 2 angles whose sum is 90Ĭomp.=90-x Supplementary Angles 2 angles whose sum is 180 The measure of angle CAX=1/2 the measure of angle BAC Definition of Angle-Bisector Theorum measure of angle BAX=measure of angle CAX Postulate statements accepted as true, without proof, opposites of theorums Segment Addition Postulate SAP, if B is between segment AC, then AB+BC=AC angle geometric figure formed by 2 rays without a common endpoint acute angles angle measure is between 0-90 right angles angle measure is 90 straight angles angle measure is 180 obtuse angles angle measure is greater that 90 congruent angles "measure of angle ABC equals measure of angle XYZ" adjacent angles 2 angles that share the common vertex and one side, but not interior points angle bisector ray that divides an angle into 2 congruent angles Angle Addition Postulate AAP, if D is in the interior of angle ABC, then the measure of angle ABD+the measure of angle DBC=the measure of angle ABC Postulate 1 through any 3 points there exists a plane, through any non collinear points there is exactly one plane Postulate 2 a line contains at least 2 points, a plane contains at least 3 non collinear points, a space contains at least 4 non collinear points Postulate 3 through any 2 points there is exactly 1 line Postulate 4 if 2 planes intersect, then their intersection is a line Postulate 5 if 2 lines intersect, then exactly one plane contains the intersecting lines Theorum 1 if 2 lines intersect, then their intersection is a point Theorum 2 if there is a line and a point not on the line, then there exists a plane Theorum 3 if 2 lines intersect, then they're contained in the same plane theorums statements that require proof, use definitions/postulates/other proven theorems to prove Addition Property of Equality if a=b and c=d, then a+c=b+d Subtraction Property of Equality if a=b and c=d, then a-c=b-d Multiplication Property of Equality if a=b, then ac=bc Division Property of Equality if a=b, then a/c=b/cĬ does not equal 0 Substitution Property of Equality if A=B, then you can replace any A with any B Distributive Property of Equality a(b+c)=ab+ac Reflexive Property a=a, angle 1 is congruent to angle 1 Symmetric Property if a=b, then b=a Transitive Property (substitution) if a=b, b=c, then a=c Midpoint Theorum if M is the midpoint of segment AB, then AM=1/2AB or MB=1/2AB Definition of Midpoint Theorum if M is the midpoint of AB, then AM=MB or segment AM is congruent to segment MB Angle-Bisector Theorum if segment AX bisects angle BAC, then the measure of angle BAX=1/2 the measure of angle BAC ![]()
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