Angle with measure less than 90°

Ex: [image]

Angle with measure between 90° and 180°

Examples:

[image]

Angle with measure of 180°

[image]

Angles that share a side and do not overlap

[image]

a figure (ray, line, segment) that cuts an angle into 2 equal angles (2 halves)

ray AB is a bisector:

[image]

points on the same line

points A, B, and C are collinear

[image]

on the same plane

coplanar points:

[image]

coplanar lines:

[image]

Two angles whose measures add up to 90°, 

may or may not be adjacent

[image]  or      [image]

two angles whose measures add up to 180°,

may or may not be adjacent

[image]    or   [image]

angles with the same measure

[image]

Segments with the same length

[image]

Two adjacent angles that are supplementary

(angles that a side and whose measures add up to 180º)

[image]

Lines that intersect to form a 90° angle

[image]

a figure (ray, line, segment) that intersects with a segment to form a 90° angle and cuts it into two equal parts

goes through the midpoint and is perpendicular

[image]

location, represented with a dot 

no thickness

[image]

Set of all points on a straight path that extends in both directions infinitely

has no thickness

[image]

Set of all points on a flat surface, extends in all directions infinitely

no thickness

[image]

2

Ex: line AB

3

Ex: Plane ABC

set of all points extending from an endpoint in one direction infinitely

[image]

2

Ex: ray AB

Part of a line

Set of all points between two endpoints

[image]

A figure (ray, segment, line) that cuts a segment into two equal pieces

[image]

Space

the common endpoint of the two rays that make up an angle

[image]

Angles that are opposite each other, made of opposite rays

[image]

angles 1 and 3 are vertical

angles 2 and 4 are vertical

The part of a conditional statement that follows the "if", sets the stage.

"p"

Ex: If I study, then I will learn.

Hypothesis: I study.

The part of a conditional statement that follows the "then".

"q"

Ex: If I study, then I learn.

Conclusion: I learn.

A statement in "if, then" form.

Ex: If I study, then I learn.

Negate and switch the hypothesis and conclusion of a conditional statement.

Ex:   

Conditional: If I study, then I learn.

Contrapositive: If I don't learn, then I didn't study.

Switch the hypothesis and conclusion of a conditional statement.

Ex:

Conditional:  If I study, then I learn.

Converse: If I learn, then I studied.

Negate the hypothesis and conclusion of a conditional statement.

Ex:

Conditional: If I study, then I learn.

Inverse: If I don't study, then I don't learn.

An example that proves a rule is incorrect.

Ex:  All supplementary angles are adjacent.

Counterexample:  any supplementary angles that aren't adjacent

[image]

p --> q

p

therefore q

Law of Detachment

If you are given a rule, then told p is true, q is automatically true

p --> q

q --> r

therefore p -->r

Law of Syllogism (Chain Rule)

p leads to q and q leads to r, so p eventually leads to r

lines in the same plane that do not intersect

[image]

Lines in different planes (won't intersect)

[image]

║

alternate exterior angles

a pair of angles that lie outside two lines on opposite sides of the transversal

when lines are parallel, alternate exterior angles are congruent

Angles 1 and 7, Angles 2 and 8

[image]

a pair of angles that line inside lines on opposite sides of the transversal

when lines are parallel, alternate interior angles are congruent

Angles 4 and 6 and Angles 3 and 5

[image]

a pair of angles inside the lines on the same side of the transversal

when lines are parallel, consecutive interior angles are supplementary

Angles 4 and 5 and Angles 3 and 6

[image]

an interior and an exterior angle that are on the same side of the transversal

when lines are parallel, corresponding angles are congruent

Angles 1 and 5, Angles 2 and 6, Angles 4 and 8, Angles 3 and 7

[image]

Angles 1 and 5

[image]

Angles 2 and 8

[image]

Angles 4 and 6

[image]

Angles 4 and 5

[image]

y- y₁=m(x-x₁)

m= slope

x₁= x-coordinate

y₁= y-coordinate

y=mx+b

m=slope

b= y-intercept

a line that cuts through 2 others

t is the transversal

[image]

What is the meaning of 

    __

      AB ?

What is the meaning of 

[image]