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Geometry Vocabulary Use Segments and Congruence Midpoint and Distance Formulas
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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

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.

- 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

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