Season 01 • Episode 14 • Vectors and configurations
0Vectors and configurations
Season 01
Episode 14 Time frame 1 period
Prerequisites :
Basinotionsaboutvetors.Objectives :
•
Disover some simplebut importantongurations involvingvetors.•
Pratise the voabulary about geometry.Materials :
•
Hand-outs withall the ongurations and properties.•
Properties involvingvetorsand gures.1 – Matching game 10 mins
Eah student is handed out a ard with either a property involving vetors or a gure.
Students mingle tond who has the rightproperty for their gureand vie-versa.
2 – Writing a property 15 mins
Eahpairhastowriteapreiseruleabout thepropertyand gurethey have.The teaher
heks eah one of them.
3 – Presentations 30 mins
Eah pair goes to the board to explain their property. A hand-out with all properties is
given at the end of the session.
Vectors and configurations
Document Summary
A quadrilateral
ABCD
is a parallelogram if and onlyif− − − − − →
AB =
− − − − − →
DC.
b
A
b B
b
C
b D
A quadrilateral
ABDC
is a parallelogram if and onlyif− − − − − →
AB =
− − − − − →
CD.
b
A
b B
b D
b C
For any three points
A
,B
andC
,− − − − − →
AB +
− − − − − →
BC =
− − − − − →
AC.
b
A
b
B
b
C
A quadrilateral
ABCD
is a parallelogram if and onlyif− − − − − →
AB +
− − − − − →
AD =
− − − − − →
AC.
b
A
b
B
b
D
b
C
Apoint
A
isthemidpointofasegmentBC
if and onlyif
− − − − − →
AB +
− − − − − →
AC = → 0. b
B
b
C
b
A
Season 01 • Episode 14 • Vectors and configurations
2Apoint
C
isthemidpointofasegmentAB
if and onlyif
− − − − − →
AB = 2
− − − − − →
AC. b
A
b
B
b
C
The fat that the lines
CD
andAB
are parallel,that thevetorshavethe same di-retionandthat
CD = 2AB
anbewritten as the equality− − − − − →
CD =
− − − − − − − − →
2AB.
b
A b
B
b
C
b
D
Ifpoint
B
isthemidpointofasegmentAC
, then for any pointM
,− − − − − − →
M A +
− − − − − − − →
M C = 2
− − − − − − − →
M B.
b
M
b
A
b C
b
B
Ifthe points
B
andC
are the midpointsof the legs of atriangleADE
, then− − − − − →
DE = 2
− − − − − →
BC.
b
A
b
D b
E
b
B
b
C
If
