Mathematics, 23.10.2020 18:00, biggy54
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.
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
AO = OC because it is given that diagonals bisect each other.
BO = OD because it is given that diagonals bisect each other.
For triangles AOB and COD, angle 1 is equal to angle 2, as they are .
Therefore, the triangles AOB and COD are congruent by SAS postulate.
Similarly, triangles AOD and COB are congruent.
By CPCTC, angle ABD is equal to angle BDC and angle ADB is equal to angle DBC.
As the alternate interior angles are congruent, the opposite sides of quadrilateral ABCD are parallel.
Therefore, ABCD is a parallelogram.
Which is the missing phrase in Terra's proof?
alternate interior angles
corresponding angles
same-side interior angles
vertical angles
Answers: 1
Mathematics, 21.06.2019 22:30, smarty5187
One number is 4 less than 3 times a second number. if 3 more than two times the first number is decreased by 2 times the second number, the result is 11. use the substitution method. what is the first number?
Answers: 1
Mathematics, 21.06.2019 23:50, BreBreDoeCCx
You so much whoever answers with accuracy β’the parent function of the graph of f(x) is the square root function, which was reflected across the x-axis. which of the following is the equation of f(x)?
Answers: 1
Look at the quadrilateral shown below:
A quadrilateral ABCD is shown with diagonals AC and BD inter...
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