Geometry Proof Justifications

26 terms by Guonine 

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Theorems, postulates and definitions

Midpoint

If a point is the midpoint of a segment, then it divides rhe segment into two congruent parts.

Complements of the same angle are congruent

If two angles are each complementary to a third angle, then they're congruent to each other.

Complements of congruent angles are congruent

If two angles are complementary to two other congruent angles, then they're congruent.

Supplements of the same angle are congruent

If two angles are supplementary to the same angle, then they're congruent.

Supplements of congruent angles are congruent

If two angles are supplementary to two other congruent angles, then they're congruent to each other.

Perpendicular

If segments are perpendicular, then they form right angles.

Complementary angles

If two angles are complementary to each other, then they form a right angle.

supplementary angles

if two angles are supplementary to each other, then they form a straight line.

segment addition (three total segments)

if a segment is added to two congruent segments, then the sums are congruent.

angle addition (three total angles)

if an angle is added to two congruent angles, then the sums are congruent.

segment addition (four total segments)

if two congruent angles are added to two other congruent angles, then the sums are congruent.

angle addition (four total angles)

if two congruent angles are added to two other congruent angles, then the sums are congruent

bisect

if an angle is bisected, then it's divided into two congruent segments.

trident

if an angle is trisected, then it's divided into three congruent parts.

segment subtraction (three total segments)

if a segment is subtracted from two congruent segments, then the differences are congruent.

angle subtraction (three total segments)

if an angle is subtracted from two congruent angles, then the differences are congruent.

segment subtraction (four total segments)

if two congruent segments are subtracted from two other congruent segments, then the diferences are congruent.

angle subtraction (four total angles)

if two congruent angles are subtracted from two other congruent angles, then the differences are equal.

like multiples

if two segments (or angles) are congruent, then their like multiples are congruent.

like divisions

if two segments (or angles) are congruent, then their like divisions are congruent

vertical angles are congruent

if two angles are vertical angles, then they're congruent.

transitive property (for three segments or angles)

if two segments (or angles) are congruent to a third segment or angle, then they're congruent to each other.

transitive property (for four segments or angles)

if two segments or angles are congruent to congruent segments or angles, the they're congruent to each other.

substitution property

if two geometric objects are congruent, then you can substitute one for the other.

SSS

(side-side-side) if three sides of a triangle are congruent to three sides of another triangle, then the triangles are congruent.

SAS

(side-angle-side) of two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the. the triangles are congruent.

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