Elba writes the following proof for the theorem: if the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram: elba's proof 1. for triangles aob and cod, angle 1 is equal to angle 2 as they are vertical angles. 2. ao = oc and bo = od because it is given that diagonals bisect each other. 3. therefore, the triangles aob and cod are congruent by sas postulate. 4. similarly, triangles aod and cob are congruent. 5. by cpctc, angle abd is equal to angle cdb and angle adb is equal to angle cbd. 6. as the are congruent, the opposite sides of quadrilateral abcd are parallel. 7. therefore, abcd is a parallelogram. which is the missing phrase in elba's proof? alternate interior angles corresponding angles corresponding sides opposite sides

answer: as the alternate interior angles are congruent, the opposite

sides of quadrilateral abcd are parallel.

step-by-step explanation:

so, the missing phrase in elba's proof is: alternate

interior angles

let's break this statement up so we can find the answer:

by cpctc, angle abd is equal to angle cdb and angle adb is

equal to angle cbd.

since

angle abd is equal to angle cdb, this means that they are alternate interior angles

so, the correct answer would be: as the alternate interior angles are congruent, the opposite

sides of quadrilateral abcd are parallel.

two interior angles which lie on opposite sides of a

transversal   and on different parallel

lines and are called alternate interior angles.

hello,

elba writes the following proof for the theorem: if the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram:

elba's proof

1. for triangles aob and cod, angle 1 is equal to angle 2 as they are vertical angles.

2. ao = oc and bo = od because it is given that diagonals bisect each other.

3. therefore, the triangles aob and cod are congruent by sas postulate.

4. similarly, triangles aod and cob are congruent.

5. by cpctc, angle abd is equal to angle cdb and angle adb is equal to angle cbd.

6. as the are congruent, the opposite sides of quadrilateral abcd are parallel.

7. therefore, abcd is a parallelogram.

which is the missing phrase in elba's proof?

answer - opposite

the right system of equations to describe the situation would

be on the form:

x1 = 8000 + y1*t

and

x2 = 8000 + y2*t

where x1 and x2 represents the total money of imogene and her

friend respectively at the end of t years.

now for the value of amount earned, y1 and y2:

y1=8000*0.08

y2=2000*√(t-2)

-14 is the answer

hope this : ))