represents a position in space or on a plane

has no size represented by a dot

labeled with an upper case letter

. P

figure that extends forever in 2 directions

NO ENDPOINTS

Named with any 2 of its points' letters under a ↔  OR

by line and an italiziced letter put near line to name.

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line segment or simply

segment

part of a line that is between and including 2 endpoints

Named by its 2 endpoints in any order under ‾‾.

Part of line that is on one side of a point of that line.

Named with its initial (or ENDPOINT) FIRST and then any point through which the ray goes under a  →.

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points that could lie on one line.

Here, the red points are collinear, the gray points are noncollinear because they cannot all lie on only 1 line

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the common point or points shared by 2 figures

[image] E is the intersection of line AD and line BC.

[image]  The blue line is the intersection of plane M and plane S.

length of segment MJ

distance between Points M and J .

if on a number line the absolute value of the difference of the coordinates of the endpoints.

| coordinate of M minus coordinate of J|

Will always be positive or 0.

BE CAREFUL WITH NEGATIVES.

If C is between A and B, then AC + CB = AB.

part segment + other part = entire segment in question

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segments, angles or figures having equal SIZE AND SHAPE.

 @  means congruent

Congruent segments are shown on drawings by the same number of tick marks on congruent segments.

Congruent angles are shown the same way OR by having the same number of arcs.

The point that divides a segment into 2 congruent segments. If M is the midpoint of segment AB

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 AM = MB

figure formed by 2 rays that share the same initial or endpoint.

Rays are the sides, vertex is point shared by both.

Angles are named with a single number or the letter for the vertex point if they are isolated. If it is not clear which angle is meant,  3 letters are needed:  the letters for the vertex and a point on each side of the angle.  This angle could be named ÐACB, ÐBCA orÐC

A complete rotation contains 360°.

Ancients believed that it took the sun 360 days to circle the earth.

Be glad that they did not know that it takes 365 1/4 days for the earth to circle the sun.

Degrees measure how open an angle is, not how long the sides are.

straight angle

An angle that forms a straight line with its vertex somewhere on that line.

It contains half a rotation or half of 360°.

A straight angle contains 180°.[image]

an angle that contains 1/4 of a complete rotation or 90°.

The corner of this index card is a right angle.

A square box inside an angle shows that the angle is a right angle.

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An angle that is more than 0°   and less than 90 ° .

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These are cute, little angles.

An angle that is more than 90° and less than 180 °

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This angle is obese or bigger than a right angle, but less than

a straight angle.

the length between 2 points P₁ and P₂ on a Cartesian graph.

Label the coordinates CAREFULLY

( x₁, y₁) and (x₂, y₂).        

Then sub into

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If A (x₁, y₁) and B (x₂,y₂) are points in a coordinate plane, then the midpoint of line segment AB has the coordinates

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if M is the midpoint of AB, then      

   AM = MB = ½  of AB

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 a ray that divides an angle into 2 adjacent angles that are congruent ( have equal measures)

Ray BD bisects ÐABC since it divides the angle into 2 congruent angles ÐABD and ÐDBC;         mÐABD = mÐDBC

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When 2 lines intersect, the 2 pairs of opposite angles are vertical Ðs.  Form BUTTERFLY WINGS or

A BOWTIE

Ð1 & Ð3are vertical Ðs  ; Ð2 &Ð4 are vertical Ðs

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If point D is in the interior ofÐABC,

then mÐABD + mÐDBC =  mÐABC

m partÐ+ m partÐ =m entireÐ

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the 2 Ðs formed when the endpoint of a ray falls on a line.

(2 adjacent Ðs whose noncommon sides are opposite rays.)

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Ð ADB and ÐBDC form a linear pair and will add to 180°

Special case of angle addition. 

2 angles whose measures add to 90 ^o

Complementary  Corner   Add to 90^o

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 two angles whose measures add to 180 degrees.

Supplementary make a  Straight Line

and/or Add to 180^o

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angles that share a common vertex and side, but no interior points

2 lines that intersect to form right angles.

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Symbol:  ^

 GE ^ DF

Add the coordinates of the endpoints.

Then, divide that sum by 2 to get the midpoint.

x₂ - x₁

2

To find an endpoint when given a midpoint and one endpoint coordinates

Label midpoint coordinates (x_M  , y_M )

Label given endpoint (x₁  , y₁ )

You are looking for (x₂  , y₂ )other endpoint

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