Geometry Exam 2 Topic List PDF

The Bronx High School of Science Mathematics Department Rachel Hoyle, Principal Colin Morrell, Assistant Principal Course: Geometry Teacher: Mr. Cervone **Topic List for Exam 2** **Geometry as a Postulational System** *1. Undefined Terms* Points Lines Planes Space 2\. *Definitions*...

The Bronx High School of Science Mathematics Department Rachel Hoyle, Principal Colin Morrell, Assistant Principal Course: Geometry Teacher: Mr. Cervone **Topic List for Exam 2** **Geometry as a Postulational System** *1. Undefined Terms* Points Lines Planes Space 2\. *Definitions* [Definition]: A definition is a statement that clarifies or explains the meaning of a word or a phrase. Definitions are usually biconditional statements. [Undefined Terms]: Undefined terms are descriptions of primitive notions. A primitive notion is not defined in terms of previously defined concepts but described using intuition. [Collinear Points]: Collinear Points are points that lie on the same line. [Coplanar Points]: Coplanar points are points and / or lines that lie on the same plane. [Postulate]: Something that is accepted as true without explanation or proof (i.e. a basic principle). [Theorem]: A statement which can be proven using postulates, definitions, and other theorems. Theorems are either conditional statements or sometimes biconditional statements. [Congruence]: Two segments are congruent if and only if they have the same measure. *AB BC AB BC* ≅↔= [Segment Bisector]: A bisector of a segment is a line that intersects the segments at its midpoint. [Midpoint]: A midpoint of a segment is a point that divides the segment into two congruent segments. [Equivalence Relation]: A relation is an equivalence relation if and only if it satisfies the reflexive, symmetric, and transitive property at the same time. [Angle]: An angle is formed if and only if two rays intersect at their endpoint. [Perpendicular Lines]: Two lines are perpendicular if and only if the two lines intersect to form right angles. [Right Angle]: An angle is a right angle if and only if the angle measures 90°. [Adjacent Angles]: Two angles are adjacent if and only if they share the same ray and vertex. [Linear Pair]: Two adjacent angles are a linear pair if and only if the angles are supplementary. [Supplementary Angles]: Two angles are supplementary if and only if the measure of those two angles add up to 180⁰. [Complementary Angles]: Two angles are complementary if and only if the measure of those two angles add up to 90⁰. [Angle Bisector]: A ray is an angle bisector if and only if its endpoint is the vertex of the angle, and that divides the angle into two congruent angles. [Vertical Angles]: Two angles are vertical if and only if the sides of one angle are the opposite rays (two intersecting straight lines) of the sides of the other angle. Page \| **1** The Bronx High School of Science Mathematics Department Rachel Hoyle, Principal Colin Morrell, Assistant Principal Course: Geometry Teacher: Mr. Cervone *3. Postulates & Properties* [Partition Postulate]: The whole is equal to the sum of its parts. For example: *AB BC AC* + = or *m AOB m BOC m AOC* ∠ +∠ =∠ [Segment Addition Postulate]: For example: *AB BC AC* + ≅ [Angle Addition Postulate]: For example: ∠ +∠ ≅∠ *AOB BOC AOC* [Reflexive Property]: Any object is associated with itself [Symmetric Property]: If "a" is associated with "b", then "b" is associated with "a". [Transitive Property]: If "a" is associated with "b" and "b" is associated with "c", then "a" is associated with "c". [Addition Postulate]: o If equal [quantities] are added to equal quantities, the sums are equal. o If congruent [segments] are added to congruent segments, the sums are congruent. o If congruent [angles] are added to congruent angles, the sums are congruent. [Subtraction Postulate]: o If equal [quantities] are subtracted from equal quantities, the differences are equal. o If congruent [segments] are subtracted from congruent segments, the differences are congruent. o If congruent [angles] are subtracted from congruent angles, the differences are congruent [Multiplication Postulate]: If equal [quantities] are multiplied by equal quantities, the products are equal. [Division Postulate]: If equal [quantities] are divided by equal quantities, the quotients are equal. *4. Theorems* If two angles are right angles, then they are congruent. If two angles are straight angles, then they are congruent. If two angles are complements of the same angle, then they are congruent. If two angles are congruent, their complements are congruent. If two angles are supplements of the same angle, then they are congruent. If two angles are congruent, then their supplements are congruent. If two angles form a linear pair, then they are supplementary. If two angles are vertical angles, then they are congruent. Angle Bisector Theorem: A bisector of an angle divides the angle into two angles, each of which has measure half that of the given angle. If the exterior sides of two adjacent angles are perpendicular, then the angles are complementary. If the exterior sides of two adjacent angles are opposite rays, then the angles are supplementary If two angles are vertical angles, then they are congruent. Two lines are perpendicular if and only if they intersect to form congruent adjacent angles. *Convention:* o *AB* = measure of distance *A* and *B* o *AB* =segment with endpoints *A* and *B*  ~=line\ containing\ *A*\ and\ *B*\ (line\ extends\ infinitely\ in\ both\ directions)~ o *AB*  ~=\ ray~ o *AB* o ≅ congruent o \|\| parallel o ⊥ perpendicular Page \| **2**