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.

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step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.