points, lines and planes

lines, segments, and rays

collinear, coplanar, shapes

postulates, theorems, and definitions

Always

Sometimes

Never

plane; collinear

line; collinear

plane; non-collinear

line; non-collinear

$$\overrightarrow{SR}$$

$$\overline{RS}$$

$$\overrightarrow{RS}$$

$$\overline{QR}$$

$$\overrightarrow{RQ}$$

$$\overrightarrow{QR}$$

$$\overrightarrow{FE}$$ and $$\overrightarrow{FG}$$

$$\overrightarrow{EF}$$ and $$\overrightarrow{FG}$$

$$\overleftarrow{FE}$$ and $$\overrightarrow{FG}$$

$$\angle K$$  

$$\angle KVJ$$  

$$\angle LVK$$  

$$\angle JKV$$  

6

4

14

8

x=3/17 ∠ABD = 27°

x=9 ∠ABD = 81°

x=3 ∠ABD = 27°

x= -3 ∠ABD = -27°

$$\angle MJN$$  

$$\angle NJP$$  

$$\angle FGE$$  

$$\angle LJK$$  

x + 3x-12=180

x = 3(180 - x) - 12

x = 3(x - 12)

x + 3(x - 12) = 180

90 - 3x - 2 = 2x + 17

3x - 2 = 2x + 17

3x - 2 = 90

3x - 2 + 2x 17 = 90

patterns

specific cases

observed examples

facts, definitions, accepted properties, and laws of logic

If x = 5 and and x = y, then y = 5.

If x = y then y = x

x = x

If 2x + 4 = 2, then x = -1

Definition of congruence

Reflexive Property of Congruence

Segment Addition Postulate

Definition of Midpoint

Addition Property of Equality

Subtraction Property of Equality

Substitution Property of Equality

Complementary Angles are Congruent

Substitution Property

Symmetric Property

Transitive Property

Reflexive Property

RS + RS = RT

ST + ST = RT

RS + ST = RT

RS = ST

Congruent Complements Theorem

Congruent Supplements Theorem

Definition of Complementary

Definition of Congruence