# Geometry Definitions, Postulates, and Theorems

Topics: Triangle, Angle, Geometry Pages: 10 (3334 words) Published: August 8, 2013
Geometry Definitions, Postulates and Theorems

Definitions Name Complementary Angles Supplementary Angles Theorem Vertical Angles Transversal Corresponding angles Same-side interior angles Alternate interior angles Congruent triangles Similar triangles Angle bisector Segment bisector Legs of an isosceles triangle Base of an isosceles triangle Equiangular Perpendicular bisector Altitude

Definition Two angles whose measures have a sum of 90o Two angles whose measures have a sum of 180o A statement that can be proven Two angles formed by intersecting lines and facing in the opposite direction A line that intersects two lines in the same plane at different points Pairs of angles formed by two lines and a transversal that make an F pattern Pairs of angles formed by two lines and a transversal that make a C pattern Pairs of angles formed by two lines and a transversal that make a Z pattern Triangles in which corresponding parts (sides and angles) are equal in measure Triangles in which corresponding angles are equal in measure and corresponding sides are in proportion (ratios equal) A ray that begins at the vertex of an angle and divides the angle into two angles of equal measure A ray, line or segment that divides a segment into two parts of equal measure The sides of equal measure in an isosceles triangle The third side of an isosceles triangle Having angles that are all equal in measure A line that bisects a segment and is perpendicular to it A segment from a vertex of a triangle perpendicular to the line containing the opposite side Page 1 of 11

Definitions, Postulates and Theorems
Definitions Name Geometric mean Definition Visual Clue The value of x in proportion a/x = x/b where a, b, and x are positive numbers (x is the geometric mean between a and b) For an acute angle of a right triangle, the ratio of the side opposite the angle to the measure of the hypotenuse. (opp/hyp) For an acute angle of a right triangle the ratio of the side adjacent to the angle to the measure of the hypotenuse. (adj/hyp) For an acute angle of a right triangle, the ratio of the side opposite to the angle to the measure of the side adjacent (opp/adj)

Sine, sin Cosine, cos Tangent, tan

Algebra Postulates Name Addition Prop. Of equality Subtraction Prop. Of equality Multiplication Prop. Of equality Division Prop. Of equality Reflexive Prop. Of equality Symmetric Property of Equality Substitution Prop. Of equality Transitive Property of Equality Distributive Property

Definition If the same number is added to equal numbers, then the sums are equal If the same number is subtracted from equal numbers, then the differences are equal If equal numbers are multiplied by the same number, then the products are equal If equal numbers are divided by the same number, then the quotients are equal A number is equal to itself If a = b then b = a If values are equal, then one value may be substituted for the other. If a = b and b = c then a = c a(b + c) = ab + ac

Visual Clue

Congruence Postulates Name Definition Reflexive Property of Congruence A ≅ A Symmetric Property of If A ≅ B, then B ≅ A Congruence Transitive Property of Congruence If A ≅ B and B ≅ C then A≅C Page 2 of 11

Visual Clue

Definitions, Postulates and Theorems
Angle Postulates And Theorems Name Definition Angle Addition For any angle, the measure of the whole is postulate equal to the sum of the measures of its nonoverlapping parts Linear Pair Theorem If two angles form a linear pair, then they are supplementary. Congruent If two angles are supplements of the same supplements theorem angle, then they are congruent. Congruent If two angles are complements of the same complements angle, then they are congruent. theorem Right Angle All right angles are congruent. Congruence Theorem Vertical Angles Vertical angles are equal in measure Theorem Theorem If two congruent angles are supplementary, then each is a right angle. Angle Bisector If a point is on the bisector of an...