According to the Journal of Irreproducible Results, any obtuse angle is a right angle! Here is their argument. Given the obtuse angle x, we make a quadrilateral ABCD with DAB = x, and ABC = 90◦, andAD = BC. Say the perpendicular bisector toDC meets the perpendicular bisector to AB at P. ThenPA = PB andPC = PD. So the trianglesPADandPBC have equal sides and are congruent. Thus PAD = PBC. But PAB is isosceles, hence PAB = PBA. Subtracting, gives x = PAD− PAB = PBC − PBA = 90◦. This is a preposterous conclusion – just where is the mistake in the “proof” and why does the

Question

According to the Journal of Irreproducible Results, any obtuse angle is a right angle! Here is their argument. Given the obtuse angle x, we make a quadrilateral ABCD with DAB = x, and ABC = 90◦, andAD = BC. Say the perpendicular bisector toDC meets the perpendicular bisector to AB at P. ThenPA = PB andPC = PD. So the trianglesPADandPBC have equal sides and are congruent. Thus PAD = PBC. But PAB is isosceles, hence PAB = PBA. Subtracting, gives x = PAD− PAB = PBC − PBA = 90◦. This is a preposterous conclusion – just where is the mistake in the “proof” and why does the

Answer 1

i like to eat A is in PDC nuggets

Answer 2

The mistake in the "proof" lies in assuming that the perpendicular bisector of DC is guaranteed to intersect the perpendicular bisector of AB at point P. This assumption is not true for all obtuse angles.

To see why this assumption is flawed, consider an obtuse angle greater than 90 degrees (let's call it angle x). In this case, forming the quadrilateral ABCD with DAB = x and ABC = 90 degrees is possible.

However, the perpendicular bisector of DC will never intersect the perpendicular bisector of AB. The perpendicular bisector of DC is a vertical line, while the perpendicular bisector of AB is a horizontal line. These two lines will never intersect, and therefore, point P cannot be determined.

Without point P, the argument presented in the "proof" breaks down, and we cannot conclude that x is equal to 90 degrees. Therefore, the claim that any obtuse angle is a right angle is incorrect.

Answer 3

The mistake in the "proof" lies in assuming that the perpendicular bisectors to DC and AB intersect at point P. This assumption is incorrect.

To understand why, let's analyze the situation step by step:

1. The quadrilateral ABCD is created with angles DAB = x and ABC = 90 degrees, and AD = BC.

2. The perpendicular bisector of DC and the perpendicular bisector of AB are constructed.

3. The assumption is made that these two perpendicular bisectors intersect at point P.

4. Based on this assumption, it is then claimed that PA = PB and PC = PD.

5. It is further claimed that triangles PAD and PBC have equal sides and are congruent.

6. From the congruence of triangles PAD and PBC, it is concluded that PAD = PBC.

7. By considering the isosceles triangle PAB, it is stated that PAB = PBA.

8. Subtracting PAB from PAD and PBA from PBC, it is then incorrectly concluded that x = PAD - PAB = PBC - PBA = 90 degrees.

The mistake occurs in step 3, where the assumption of the intersection of the perpendicular bisectors is made. In reality, there is no guarantee that the perpendicular bisectors of DC and AB will intersect at a single point. Without this intersection, the subsequent claims regarding congruence and equality fall apart.

Therefore, the assumption made in the argument is invalid, rendering the conclusion that any obtuse angle is a right angle preposterous.

Answer 4

So the trianglesPADandPBC have equal sides and are congruent ---> flawed

You have 2 sides of one equal to 2 sides of the other, but no angles equal, so you cannot say they are congruent. (You need either SAS )

Anything after that is bogus.