Postulates,+Theorems,+and+Know+it+Notes

=__**Chapter 1 Postulates, Theorems, and Know- it Notes: Sections 1-7**__=

Section 1-1 (Gregg)

 * 1-1-1:** Through any two points there is exactly one line.
 * 1-1-2**: Through any three noncollinear points there is exactly one plain containing them.
 * 1-1-3:** If two points lie in a plane, then the line containning those points lies on the plane.
 * 1-1-4**: If two lines intersect, then they intersect in exactly one point.
 * 1-1-5**: If two planes intersect, then they intersect in exactly one line.

**Section 1-2 (Adnan)**

 * 1-2-1:** The points on a line can be put into a one-to-one correspondence with real numbers.
 * 1-2-2:** If B is between A and C, then AB + BC = AC

Section 1-3 (Hayley)

 * 1-3-1:** Given Line AB and a point O on AB, all rays that can be drawn from O can be put into a one-to-one correspondence with the real numbers from 0 to 180
 * 1-3-2:** If S is in the interior of Angle PQR, then m∠PQS + m∠SQR = m∠PQR. (∠ Add. Post.)

**Section 1-6 (Tyler)**
**Mid Point Formula**: 
 * Distance Formula**: 
 * Pythagorean Theorem**:

= __Chapter 2 Postulates, Theorems, and Know-it Notes: Sections 1-7__ = Section 2-2 (Erin) ** Conditional Statements
 * By phrasing a conjecture as an if-then statement, you can quickly identify its hypothesis and conclusion.
 * “If p, then q” can also be written as “if p, q”, “q, if p,”, “p implies q,”, and “p only if q.”
 * To show that a conditional statement is false, you need to find only one counterexample where the hypothesis is true and the conclusion is false.
 * The negation of a true statement is false, and the negation of a false statement is true. Negations are used to write conditional statements.
 * A conditional and its contrapositive are logically equivalent, and so are the converse and inverse.
 * [[image:https://www.wikispaces.com/i/c.gif width="22" height="22" caption="Bold"]]The converse of a true conditional is not necessarily false. All four related conditionals cam be true, or all four can be false, depending on the statement.

Section 2-4

 * ======For a biconditional statement to be true, both the conditional statement and its converse must be true. If either the conditional or the converse is false, then the biconditional statement is false.======
 * ======p <—>q means p → q and q → p======
 * ======biconditional statements are used to write definitions.======

Section 2-5 (Remy)

 * **Linear Pair Theorem:** If two angles form a linear pair, then they are supplementary.
 * **Congruent Supplements Theorem:** If two angles are supplementary to the the same angle (or to two congruent angles), then the two angles are congruent.
 * **Right Angle Congruence Theorem:** All right angles are congruent.
 * **Congruent Complements Theorem:** If two angles are complementary to the same angle (or two congruent angles), then the two angles are congruent.
 * **//Know it Note-// The Proof Process:**
 * 1) Write the conjecture to be proven.
 * 2) Draw a diagram to represent the hypothesis of the conjecture.
 * 3) State the given information and mark it on the diagram.
 * 4) State the conclusion of the conjecture in terms of the diagram.
 * 5) Plan your argument and prove the conjecture.

Section 2-6 (T.J.)

 * **Properties of Congruence-**
 * **Reflexive Prop. Of Congruence: Figure A is congruent to Figure A**
 * **Symmetric Prop. of Congruence: if Figure A is congruent to Figure B Than figure B is congruent to Figure A**
 * **Transitive Prop. of Congruence: If Figure A is Cong. to Figure B and Figure B is Cong. to figure C than Figure A is Cong. to Figure C**

Section 2-7 (Joe B.)

 * **Vertical Angles Theorem:** Vertical angles are congruent

 =__Chapter 3 Postulates, Theorems, and Know- it Notes: Sections 1-7__=

**Section 3-1 (Hayley)**
-none

**Section 3-2 (Adnan)**

 * 3-2-1:** //Corresponding Angles Postulate -// If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.
 * 3-2-2:** //Alternate Interior Angles Theorem -// If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.
 * 3-2-3:** //Alternate Exterior Angles Theorem -// If two parallel lines are cut by a transversal, then the two pairs of alternate exterior angles are congruent.
 * 3-2-4:** //Same-Side Interior Angles Theorem -// If two parallel lines are cut by a transversal, then the two pairs of same-side interior angles are supplementary.

**Section 3-3 (Gregg)**

 * Converse of the corresponding angles postulate- If two coplanar lines are cut by a transversal so that a pair of corresponding angles are congruent, than the two lines are parallel.
 * Parallel Postulate- Through a point P not on line L, there is exactly oneline parallel to L.
 * Converse of the alternate interior angles theorum- If two coplanar lines are cut by a transversal so that a pair of alternate interior angles are congruent, then the two lines are parallel.
 * Converse of the alternate exterior angles theorum- If two coplanar lines are cut by a transversal so that a pair of alternate exterior angles are congruent, then the two lines are parallel.
 * Converse of the same side interior angles theorum- If two coplanar lines are cut by a transversal so that a pair of same side interior angles are supplementary, then the two lines are parallel.

**Section 3-6 (Tyler)**

 * The **point slope** **form** of a line is **y-y1=m(x-x1)**, where m is the slope and (x1, y1) is a given point on the line.
 * The **slope intercept form** of a line is **y=mx+b** where m is the slope and b is the y-intercept.


 * **Parallel Lines:** have the same slope but different y-intercept.
 * Example:** y=5x+8, y=5x-4


 * **Intersecting Lines:** have different slopes.
 * Example:** y=2x+5, y=4x-3


 * **Coinciding Lines:** have same slope and same y-intercept.
 * Example:** y=2x-4, y=2x-4

=__Chapter 4: Postulates, Theorems, and Know-it Notes: Section 1-8__=

Section 4-3 (Erin)
· Geometric figures are congruent if they are the same size and shape. · Corresponding angles and corresponding sides are in the same position in polygons with an equal number of sides. · Two polygons are congruent polygons if and only if their corresponding angles and sides are congruent. · Triangles that are the same size and shape are congruent. · To name a polygon, write the vertices in consecutive order. In a congruence statement, the order of the vertices indicates the corresponding parts.