Warm Up Sit in the same seats as yesterday Put your puzzle pieces together Use glue sticks on...
14
Warm Up Warm Up Sit in the same seats as Sit in the same seats as yesterday yesterday Put your puzzle pieces together Put your puzzle pieces together Use glue sticks on round table Use glue sticks on round table Use marker to go over the Use marker to go over the answers if you are having answers if you are having trouble seeing them! trouble seeing them!
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Transcript of Warm Up Sit in the same seats as yesterday Put your puzzle pieces together Use glue sticks on...
Warm UpWarm Up
Sit in the same seats as yesterdaySit in the same seats as yesterday Put your puzzle pieces togetherPut your puzzle pieces together Use glue sticks on round tableUse glue sticks on round table Use marker to go over the answers if you Use marker to go over the answers if you
are having trouble seeing them!are having trouble seeing them!
B E
A
C D
T65: If a line is || to one side of a Δ and intersects the other 2 sides, it divides those 2 sides proportionally. (Side splitter theorem)
8.5 Three Theorems Involving Proportions
Given: BE CD
Prove: =
AB
BC
AE
ED
B E
A
CD
∆ABE ~ ∆ACD AA ~
AB
AC
AE
AD
AB
AB BC EDAE
AE
=
= If a line is parallel to one side , it divides the 2 sides proportionally.Substitute: addition of two segments
AE(AB+BC) = AB(AE+ED)
NOW:Cross multiply
AEAB+AE BC=AB AE+AB ED
Proof of T65
AE BC = AB ED Subtract AB AE
AE
ED
AB
BC = Ratio of top side to bottom side.
Given: AT
BN
FA = 6, FT = 3, AT = 5, TN = 4
Find: length BN and AB
A T
F
B N
Remember to label the shape and set up proportions using corresponding sides or side splitter theorem.
Answer:Answer:
BN = 35/3BN = 35/3
AB = 8AB = 8
T66: If three or more parallel lines are intersected by two transversals, the parallel lines divide the transversals proportionally.
A B
C
E
D
FG
Given: AB CD EF
Conclusion:
AC
CE
BD
DF=
Draw AF
In Δ EAF, CEAC
= GF
AG
Bottom
Top
In Δ ABF, GFAG
= DF
BD
Substitute BD for AG and DF for GF,
substitution or transitive
CE
AC= DF
BD
T67: If a ray bisects an angle of a triangle, it divides the opposite side into segments that are proportional to the adjacent sides. (Angle Bisector Theorem)
DC
B
AGiven: ∆ ABD
AC b <BAD
Prove:
BC
CD
AB
AD=
Rightside
Rightbase
leftside
Leftbase=
Set up ProportionsSet up Proportions
AB
BC
AD
CD=
CD
BC
BC • AD = AB • CD Means Extreme
Therefore:
=AD
AB
Rightside
Rightbase
leftside
Leftbase=
Rightside
Leftside
Rightbase
Leftbase=
Given <ABD <DBC
Lengths as shown
Find: DC
A
B
CD
8 10
4
Set up segment proportions first then fill in numbers.
10
8=
x
4X = 5
