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 Terra's proof? (6 points)
alternate interior angles
Oь
corresponding angles
same-side interior angles
d
vertical angles
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 Terra's proof? (6 points)
alternate interior angles
Oь
corresponding angles
same-side interior angles
d
vertical angles
2 answers:
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