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

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evancu

Answer:

D) Vertical Angles

Step-by-step explanation:

This is due to the fact angles 1 and 2 and vertical angles. This is supported by the definition of a vertical angle.  

The missing phrase in Terra's proof is vertical angles or opposite angles.

What are opposite angles?

When two lines intersect each other, the angles formed opposite to each other are equal.

The phrase missing in Terra's proof is explained below:

Terra explains how the diagram is a parallelogram.

She says that "For triangles AOB and COD, angle 1 is equal to angle 2. as they are            ". It is not explained why these angles are equal.

These angles are equal because they are opposite angles or vertical angles.

When two lines intersect each other, the angles formed opposite to each other are equal.

Therefore, we have found that the missing phrase in Terra's proof is vertical angles or opposite angles.

Learn more about vertical angles here: https://brainly.com/question/1673457

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