Look at the quadrilateral shown below: A quadrilateral ABCD is shown with diagonals AC and BD intersecting in point O. Angle AOB is labeled as 1, angle BOC is labeled as 4, angle COD is labeled as 2, and angle AOD is labeled as 3.

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

Terra's proof

AO = OC because it is given that diagonals bisect each other.
BO = OD because it is given that diagonals bisect each other.
For triangles AOB and COD, angle 1 is equal to angle 2, as they are .
Therefore, the triangles AOB and COD are congruent by SAS postulate.
Similarly, triangles AOD and COB are congruent.
By CPCTC, angle ABD is equal to angle BDC and angle ADB is equal to angle DBC.
As the alternate interior angles are congruent, the opposite sides of quadrilateral ABCD are parallel.
Therefore, ABCD is a parallelogram.

Which is the missing phrase in Terra's proof?
alternate interior angles
corresponding angles
same-side interior angles
vertical angles

AOB and COD

Step-by-step explanation:

got the same question that was missing a different part

For triangles AOB and COD, angle 1 is equal to angle 2, as they are vertical angles.

AO = OC and BO = OD because it is given that diagonals bisect each other.

The triangles AOB and COD are congruent by SAS postulate.

Similarly, triangles AOD and COB are congruent.

By , angle ABD is equal to angle CDB and angle ADB is equal to angle CBD.

As the alternate interior angles are congruent, the opposite sides of quadrilateral ABCD are parallel.

Therefore, ABCD is a parallelogram.

u = -(6/7)w

step-by-step explanation:

place all values with 'u' on one side of the equation.

4u + 8w = - 3u + 2w

4u + 3u = 2w - 8w

further simplify the equation by solving the addition and subtraction.

7u = - 6w

make 'u' the independent variable by placing its co-efficient on the right-hand side.

u = - (6/7)w

b. y = 4x - 2

step-by-step explanation:

to find a parallel equation to an equation, make sure both equations have the same slope but different y-intercepts.

y = 4x + 1

4 = slope

1 = y-intercept

y = 4x - 2

4 = slope

-2 = y-intercept

they both have the same slope but different y-intercepts, so, b. is the correct answer.

and to check your work, you can graph both equations. : )