Mathematics, 08.11.2020 07:00 Arealbot
Look at the quadrilateral shown below:
Image Description: 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.
Melissa writes the following proof for the theorem: If the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram:
Melissa'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. The _ are congruent by SAS postulate.
4. Similarly, triangles AOD and COB are congruent.
5. By CPCTC, AB is equal to DC.
6. By CPCTC, AD is equal to BC.
7. As the opposite sides are congruent, the quadrilateral ABCD is a parallelogram.
Which is the missing phrase in Melissa's proof?
Options:
A. angles ADB and CBD
B. angles AOB and COD
C. triangles ADB and CBD
D. triangles AOB and COD
Answers: 2
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Look at the quadrilateral shown below:
Image Description: A quadrilateral ABCD is shown with diagon...
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