The following is an incomplete flowchart proving that the opposite angles of parallelogram jklm are congruent: parallelogram jklm is shown where segment jm is parallel to segment kl and segment jk is parallel to segment ml. extend segment jm beyond point m and draw point p, by construction. an arrow is drawn from this statement to angle mlk is congruent to angle pml, alternate interior angles theorem. an arrow is drawn from this statement to angle pml is congruent to angle kjm, numbered blank 1. an arrow is drawn from this statement to angle mlk is congruent to angle kjm, transitive property of equality. extend segment jk beyond point j and draw point q. an arrow is drawn from this statement to angle jml is congruent to angle qjm, alternate interior angles theorem. an arrow is drawn from this statement to angle qjm is congruent to angle lkj, numbered blank 2. an arrow is drawn from this statement to angle jml is congruent to angle lkj, transitive property of equality. two arrows are drawn from this previous statement and the statement angle mlk is congruent to angle kjm, transitive property of equality to opposite angles of parallelogram jklm are congruent. which reasons can be used to fill in the numbered blank spaces? 1alternate interior angles theorem  2alternate interior angles theorem1corresponding angles theorem  2corresponding angles  theorem  1same-side interior angles theorem  2alternate interior angles theorem1same-side interior angles theorem  2corresponding angles theorem

(B) corresponding angles theorem

Step-by-step explanation:

Given: A parallelogram JKLM is shown where segment JM is parallel to segment KL and segment JK is parallel to segment ML.

To prove: Opposite angles of parallelogram are equal.

Construction: Extend segment JM beyond point M and draw point P, Extend segment JK beyond point J and draw point Q.

Proof:

It is given that A parallelogram JKLM is shown where segment JM is parallel to segment KL and segment JK is parallel to segment ML.

Extend segment JM beyond point M and draw point P--------By construction

and Extend segment JK beyond point J and draw point Q----By construction

thus, ∠MLK≅∠PML and ∠JML≅∠QJM (Alternate interior angles theorem) (1)

Then, ∠PML≅∠KJM and ∠QJM≅∠LKJ (corresponding angles theorem)  (2)

Using equation (1) and (2) and using the transitive property of equality, we have

∠MLK≅∠KJM and ∠JML≅∠LKJ

therefore, opposite angles of the given parallelogram JKLM are congruent.

Hence proved.

the given growth  function for the length of the fish (cm) is

f(m) = 5(1.07)m = 5.35m

where 

m = months

at the end of the study, the length is 9.19 cm. the  time for conducting the study is determined as

5.35m = 9.19

m = 1.7178 months

part a.

the study was performed over a time period  of about 1.72 months. therefore  the domain for  plotting the function is 0 < = m < = 1.72.

note:

if growth  continues at this rate for up to m months, then the domain would be 0< =m< =m.

part b.

the growth function is a linear function.

when m=0, f=0.

therefore the initial growth is zero, which represents the y-intercept.

part c.

assume that the growth function is valid for 0< =m< =9.

the average rate of change of the function is the slope of the linear function, which is 5.35 cm/month.