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Geometry 2.2 Segments

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# Geometry 2.2 Segments - PowerPoint PPT Presentation

Geometry 2.2 Segments. Silly Properties. Reflexive Property For any number a: a=a Symmetric Property For any a and b: if a=b then b=a Transitive Property For any a, b, and c: if a=b and b=c then a=c. Silly Properties. Addition and Subtraction Property

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### Geometry 2.2Segments

Silly Properties
• Reflexive Property
• For any number a: a=a
• Symmetric Property
• For any a and b: if a=b then b=a
• Transitive Property
• For any a, b, and c: if a=b and b=c then a=c
Silly Properties
• Addition and Subtraction Property
• For numbers a, b, c: if a=b then a+c=b+c
• Multiplication and Division Property
• For numbers a, b, c: if a=b then axc=bxc
• Substitution Property
• For numbers a, b: if a=b then a can go anywhere that b is.
Line Segment Stuff
• If AB = 7 and BC= 12..
• Find AC
• AB + BC = AC
• 7 + 12 =

A

B

C

19

Line Segment Stuff
• If PQ = 18 and QR = 15...
• Find PR
• PQ + QR = PR
• 18 + 15 =

P

Q

R

33

Line Segment Stuff
• If LM = 22 and LN = 41...
• Find MN
• LM + MN = LN
• 22 + MN = 41
• MN = 41 – 22 =

L

M

N

19

What is in the middle?
• If three points are collinear and ...
• AD = 2 ED = 5 AE = 7
• What point is in the middle?
What is in the middle?
• If three points are collinear and ...

RS = 45 TS = 25 RT = 20

• What point is in the middle?
Easy way to do this...
• The two short measures add up to the long one.
• Look at the two shorties
• The letter they have in common is in the middle !!!
Let’s try
• XY = 15
• XZ = 7
• YZ = 22
• THE SMALL ONES ARE XY AND XZ
• THEY BOTH HAVE X
• SO X IS IN THE MIDDLE
Let’s try
• DR = 45
• GR = 19
• Dg = 26
• THE SMALL ONES ARE GR AND DG
• THEY BOTH HAVE G
• SO G IS IN THE MIDDLE
Let’s try
• Roy to Layton is 8 miles
• Layton to Salt Lake is 25 miles
• Roy to Salt Lake is 33 miles
• Which city is in the middle?