option x is ≈ option j is ∆ option 0 is º ∠ and ± and ² and ⊥ are under symbols option , is ≤ option . is ≥

### plane

an undefined term; extends without ending; no thickness; need at least 3 non collinear points to draw a plane

### adjacent ∠s

2 coplanar ∠s with a common vertex and a common side but no common interior points (don't have to be congruent)

### unnamed postulate/theorem #5

if 2 points are on a plane then the line containing those points is also on the plane

### counter example

an example used to prove a statement is false (the hypothesis is true but the statement is false) (only takes 1 counter example to prove a statement false)

### 6 properties of Equality (algebra)

addition, subtraction, multiplication, division, substitution, distributive

### midpoint theorem

parts = half the whole

( A_______M_______B) )if m is midpoint of AB then AM=1/2 AB and MB=1/2 AB)

### converse of unnamed postulate/theorem #10 (related to ⊥ lines)

if 2 lines form ≈ adjacent ∠s then they are ⊥

### unnamed postulate/theorem #11

if exterior sides of 2 adjacent acute ∠s are ⊥ then the ∠s are complementary

### unnamed postulate/theorem #14

if 2 ll planes are cut by a third plane then the lines of intersection are ll

### when dealing with Transversals and lines these 4 kinds of ∠s are formed

alt. int. ∠s

alt. ext. ∠s

same side int. ∠s

corresponding ∠s

### what types of ∠s are ≈ when 2 ll lines are cut by a trans.

corresponding ∠s are ≈ and alt. int. ∠s are ≈

### unnamed postulate/theorem #15

if a trans. is ⊥ to 1 of 2 ll lines then it is ⊥ to the other line also

### 5 ways to prove lines are ll

if 2 lines are cut by a trans. and ...

alt. int. ∠s are ≈

corresponding∠s are ≈

same side int. ∠s are supplementary;

if in a plane 2 lines are ⊥ to the same line

if 2 lines are ll to the same line

### unnamed postulate/theorem #16

though a point outside a line there is exactly 1 line ll to the given line

### unnamed postulate/theorem #17

through a point outside a line there is exactly 1 line ⊥ to the given line

### exterior ∠ theorem

the measure of the ext. ∠s of a ∆ equals the sum of the measures of the 2 remote interior ∠s

### 4 corollaries of ext. ∠ theorem

1. if 2 ∠s of 1 ∆ are ≈ of to 2 ∠s of another ∆ then the 3rd ∠s of both ∆s are ≈

2. Each ∠ of an equiangular has a measure of 60º

3. in a ∆ there can be at most 1 right or 1 obtuse ∠

4. the acute ∠s of a right ∆ are complementary

### polygon

a figure formed by coplanar segments such that 1. each segment intersects exactly with 2 other segments one at each endpoint and 2. no 2 segments with a common endpoint are collinear

### convex polygon

a polygon such that NO line containing a side of the polygon contains a point in the interior of the polygon OR a polygon is convex if NO diagonal contains points outside the polygon

### equation to find the sum of the measures of of a convex polygon

(n-2)180

(n= # of sides in the polygon)

### deductive reasoning

proving statements by reasoning from accepted postulate, definitions, theorems, and given info (must be true)

### inductive reasoning

a kind of reasoning in which the conclusion is based on several past observations (conclusion is probably true but not necessarily true)

### SSS postulate (side, side, side)

if 3 sides of one ∆ are ≈ to 3 sides of another ∆ then the ∆s are ≈

### SAS postulate (side, angle, side)

if 2 sides and the included ∠ of 1 ∆ are congruent to 2 sides and the included ∠ of the other ∆ then the ∆s are ≈

### ASA postulate (angle side angle)

if 2 ∠s and the included side of 1 ∆ are ≈ to 2 sides and included ∠s of another ∆ then the ∆s are ≈

### CPCTC (corresponding parts of ≈ ∆s are ≈)

by finding 2 ∆s ≈ then you can prove their corresponding parts are ≈

### unnamed corollary B (related to isosceles ∆s)

the bisector of the vertex ∠ of an isosceles ∆ is ⊥ the base of the midpoint

### AAS theorem (angle, angle side)

if 2 ∠s and a non included side of 1 ∆ are ≈ to the corresponding parts of the other ∆ then the ∆s are ≈

### HL theorem

if the hypotenuse and a leg of 1 right ∆ are ≈ to the corresponding parts of another right ∆ then the ∆s are ≈

### unnamed postulate/theorem #19

if a point lies on the ⊥ bisector or a segment then the point is equidistant from the endpoints of a segment

### unnamed postulate/theorem #20

if a point is equidistant from the endpoints of a segment then the point is equidistant from the sides of the ∠

### unnamed postulate/theorem #21

if a point lies on the bisector of an ∠ then the point is equidistant from the sides of the ∠

### unnamed postulate/theorem #22

if a point is equidistant from the sides of the ∠ then the point lies on the bisector of the ∠

### 3 theorems relating to parallelograms

opp. sides of a parallelogram are ≈; opp. ∠s of a parallelogram are ≈; diagonals of a parallelogram bisect each other

### 4 ways to prove the quad is a parallelogram

1. if both pairs of opp. sides of a quad. are ≈

2. if 1 pair of opp. sides of a quad are both ≈ and ll

3. if both pairs of opp. ∠s of a quad are ≈

4. if the diagonals of a quad bisect each other

### 2 unnamed postulates/theorems related to ll lines

if 2 lines are ll then all the points on 1 lines are equidistant to all the points on the other line; if 3 ll lines cut 1 transversal into ≈ segments then they cut every transversal into ≈ segments

### 2 unnamed postulates/theorems that relate to medians of a ∆

1. a line that contains the midpoint of 1 side of a ∆ and is ll to another side passes through the midpoint of the 3rd side; the segment that joins the midpoints of 2 sides of a ∆ is ll to the 3rd side and is 1/2 as long as the 3rd side

### theorems/rules about rhombuses (2)

the diagonals of a rhombus are ⊥; each diagonal of a rhombus bisects 2 ∠s if the rhombus

### unnamed postulate/theorem #23

the midpoint of the hypotenuse of a right ∆ is equidistant from the 3 vertices

### unnamed postulate/theorem #24 (related to proving a parallelogram is a rectangle)

if an ∠of a parallelogram is a right ∠ then the parallelogram is a rectangle

### unnamed postulate/theorem #25 (related to proving a parallelogram is a rhombus)

if 2 consecutive sides of a parallelogram are ≈ then the parallelogram is a rhombus

### unnamed postulate/theorem #26 (related to isosceles trap. and their base ∠s)

base ∠s of and isosceles trap are ≈

### ext. ∠ inequality theorem

the measure of an exterior ∠ of a ∆ is greater than the measure of either remote ∠s

### indirect proof

a proof in which you assume temporarily that the conclusion is not true and then deduce a contradiction

### 3 theorems/postulates regarding inequalities of 1 ∆

1. the sum of 2 sides of a ∆ is greater than the 3rd side

2. if 1 side of a ∆ is longer than the 2nd side then ∠ opp. the 1st side is larger than the ∠ opp. the 2nd side

3. if 1 ∠ of a ∆ is larger than a 2nd ∠ then the side opp. the 1st ∠ is longer than the side opp. the 2nd ∠

### SAS inequality

if 2 sides of a ∆ are ≈ to 2 sids of another ∆ but included 1st ∠ of the 1st ∆ is larger than the included ∠ of the 2nd ∆ then the 3rd side of the 1st ∆ is longer than the 3rd side of the 2nd ∆