Apartial proof was constructed given that mnop is a parallelogram. by the definition of a parallelogram, mn ∥ po and mp ∥ no. using mp as a transversal, ∠m and ∠p are same-side interior angles, so they are supplementary. using no as a transversal, ∠n and ∠o are same-side interior angles, so they are supplementary. using op as a transversal, ∠o and ∠p are same-side interior angles, so they are supplementary. therefore, and because they are supplements of the same angle. which statements should fill in the blanks in the last line of the proof?
∠m is supplementary to ∠n; ∠m is supplementary to ∠o
∠m is supplementary to ∠o; ∠n is supplementary to ∠p
∠m ≅ ∠p; ∠n ≅ ∠o
∠m ≅ ∠o; ∠n ≅ ∠p

Step-by-step explanation:

According to the problem

Which means,

And,

Therefore, the right answer is the last choice.

power property.

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