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?

2.24-7, 10-22