The flowchart shown below shows the sequence of steps to prove the theorem: Opposite angles of a parallelogram are equal:

PQ is parallel
to SR
Definition of
parallelogram
Angle 1 is
equal to angle 2
Alternate interior angles
PQRS is a
parallelogram
Given
Triangle PQS is
congruent to ROS
ASA postulate
PS is parallel
to QR
Definition of
parallelogram
Reflexive property
Angle 4 is
equal to angle 3
Alternate interior angles
Angle 5 is
equal to angle 6
CPCTC

Which is the missing statement? (6 points)

1) Angle 5 is equal to angle 5

2) Angle 5 is equal to angle 6

3) PS = QR

4) SQ = SQ

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

i believe the correct answer is b.

i hope this is what you were looking for.

see attached graph

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step-by-step explanation: