Question

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

• alternate interior angles
• corresponding angles
• same - side interior angles
• vertical angles

Explanation:

Angle 1 and angle 2 are formed by the intersection of two diagonals, making them vertical angles. Vertical angles are always congruent, which fits the requirement to prove the triangles congruent via SAS.

Answer:

vertical angles