Geometry
Vocabulary
Use Segments and
Congruence
Midpoint and Distance
Formulas
Vocab
Postulate, Axiom  Theorem
Postulate - A rule that is accepted
without proof
-
Another name for this is Axiom
If the Postulate can be proven it is called a
Theorem
Theorems are the Laws of Geometry
Vocab
Coordinate Plane
Way of Mapping Data
X – axis : Left to Right
Y – axis : Down to Up
Points: (x,y)
Locate: (3,4)
Locate: (-2,-4)
Locate: (5,-5)
Vocab
Coordinate Plane
4 quadrants:
Quadrant 1: (+,+)
Quadrant 2: (-,+)
Quadrant 3: (-,-)
Quadrant 4: (+,-)
The Origin – (0,0)
Vocab
Distance
Absolute Value of
the difference
in coordinate
values
1) Count the Units
2) What Now?
Vocab
Congruent
Congruent - Amounts / Shapes that are
equal
Why such a funny word that basically means
"equal"?
Probably because they would only be "equal" if laid
on top of each other. Anyway it comes from
Latin congruere, "to agree". So the shapes
"agree”
Vocab
Congruent
Congruent - Shapes that are equal
Vocab
Congruent Segments
Congruent Segments – Line Segments that
have equal values
Postulate
Ruler Postulate
Ruler Postulate – Points on a line can be
paired with real numbers and distance
between the two points can be found by
finding the absolute value of the difference
between the numbers. Remember all
distance measures must be positive.
Postulate
Ruler Postulate
Postulate
Ruler Postulate
Ruler Postulate – You can use a number line
to measure distance
Betweenness Theorem
If a point is between two endpoints of a line
segment, you can add the distance from the
point to one endpoint of the line segment to
the distance from the point to the other
endpoint of the line segment to get the
length of the line segment.
Betweenness Theorem
If a point is between two endpoints then I can
add the two parts to make the whole.
Formula
Segment Addition Postulate
Segment Addition Postulate
- if B is between A and C, then AB + BC = AC
Vocab
Bisector
Bisect – to cut something in half
Bisector – A geometric Figure that cuts
another figure (line segment) in half
Vocab
Segment Bisector
Segment Bisector – a point, ray, line, line
segment or plane that intersects a line
segment at its midpoint
Vocab
Midpoint
1. Midpoint – The Point of a Segment that
divides a line segment into two congruent
line segments
Formula
Midpoint Formula
Midpoint Formula – the coordinates of the
midpoint of a segment are the averages of
the x-coordinates and y-coordinates
Points: (x,y)
A: (6,3)
(x1,y1)
B: (4,9)
(x2,y2)
x1+x2 y1+y2
2
2
6+4
3+9
2
2
Midpoint: (5,6)
Formula
Midpoint Formula - Examples
A: (2,4) B: (12,2)
(x1,y1)
(x2,y2)
Midpoint: (7,3)
A: (-2,4) B: (10,-4)
(x1,y1)
(x2,y2)
Midpoint: (4,0)
x1+x2 y1+y2
2
2
2+12
4+2
2
2
x1+x2 y1+y2
2
2
-2+10 4+(-4)
2
2
Formula
Distance Formula
Distance Formula – if A (x1,y1) and B (x2,y2),
then the distance from A to B is:
Points: (x,y)
A: (6,3)
(x1,y1)
B: (4,9)
(x2,y2)
AB =
√ (x2 – x1)2 + (y2 – y1)2
AB =
√ (4 – 6)2
+ (9 – 3)2
√ (-2)2 +
AB = √
4
+
AB = √40 units or
AB =
units
(6)2
36
6.32
Formula
Distance Formula - Examples
Distance Formula – if C (x1,y1) and D (x2,y2),
then the distance from A to B is:
Points: (x,y)
C: (4,5)
(x1,y1)
D: (-2,-3)
(x2,y2)
CD =
√ (x2 – x1)2 + (y2 – y1)2
CD =
√ (-2 – 4)2
√ (-6)2
CD = √ 36
CD = √100 =
CD =
+ (-3 – 5)2
+
(-8)2
+
64
10 units
Formula
Distance Formula - Examples
Distance Formula – if E (x1,y1) and F (x2,y2),
then the distance from A to B is:
Points: (x,y)
E: (2,2)
(x1,y1)
F: (5,6)
(x2,y2)
EF =
√ (x2 – x1)2 + (y2 – y1)2
EF =
√ (5 – 2)2
√ (3)2
EF = √ 9
EF = √25 =
EF =
+ (6 – 2)2
+
(4)2
+
16
5 units