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Mathematics, 04.11.2021 05:00 myohmyohmy
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.
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
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 are congruent by SAS postulate.
Similarly, triangles AOD and COB are congruent.
By CPCTC, AB is equal to DC.
By CPCTC, AD is equal to BC.
As the opposite sides are congruent, the quadrilateral ABCD is a parallelogram.
Which is the missing phrase in Melissa's proof?
Question 14 options:
angles ADB and CBD
angles AOB and COD
triangles ADB and CBD
triangles AOB and COD
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Look at the quadrilateral shown below:
A quadrilateral ABCD is shown with diagonals AC and BD inte...
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