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Geometry Vocabulary
Use Segments and Congruence
Midpoint and Distance Formulas
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
Vocab
Ruler Postulate 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.
Ruler Postulate
Postulate
Ruler Postulate 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.
Segment Addition Postulate
Segment Addition Postulate
- if B is between A and C, then AB + BC = AC
Formula
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
Vocab
Midpoint Formula
Midpoint Formula – the coordinates of the midpoint of a segment are the averages of the x-coordinates and y-coordinates
Formula
x1+x2
2
y1+y2
2
Points: (x,y) A: (6,3)
(x1,y1)
B: (4,9) (x2,y2)
6+4
2
3+9
2
Midpoint: (5,6)
Midpoint Formula - Examples Formula
x1+x2
2
y1+y2
2
A: (2,4) (x1,y1)
B: (12,2) (x2,y2)
2+12
2
4+2
2
Midpoint: (7,3)
x1+x2
2
y1+y2
2
A: (-2,4) (x1,y1)
B: (10,-4) (x2,y2)
-2+10
2
4+(-4)
2
Midpoint: (4,0)
Distance Formula
Distance Formula – if A (x1,y1) and B (x2,y2), then the distance from A to B is:
Formula
AB = √ (x2 – x1)2 + (y2 – y1)2
Points: (x,y)
A: (6,3) (x1,y1)
B: (4,9) (x2,y2)
AB = √ (4 – 6)2 + (9 – 3)2
AB = √ (-2)2 + (6)2
AB = √ 4 + 36
AB = √40 units or 6.32 units
Distance Formula - Examples
Distance Formula – if C (x1,y1) and D (x2,y2), then the distance from A to B is:
Formula
CD = √ (x2 – x1)2 + (y2 – y1)2
Points: (x,y)
C: (4,5) (x1,y1)
D: (-2,-3) (x2,y2)
CD = √ (-2 – 4)2 + (-3 – 5)2
CD = √ (-6)2 + (-8)2
CD = √ 36 + 64
CD = √100 = 10 units
Distance Formula - Examples
Distance Formula – if E (x1,y1) and F (x2,y2), then the distance from A to B is:
Formula
EF = √ (x2 – x1)2 + (y2 – y1)2
Points: (x,y)
E: (2,2) (x1,y1)
F: (5,6) (x2,y2)
EF = √ (5 – 2)2 + (6 – 2)2
EF = √ (3)2 + (4)2
EF = √ 9 + 16
EF = √25 = 5 units