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congruent halves are just a posh way of saying 'split in two'. but these two shapes must be identical in shape, size, angles, sides etc... they must be exactly the same.

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What is the angle bisector concurrency theorem?

the definition of an angle bisector is a line that divides an angle into two equal halves. So you need only invoke the definition to prove something is an angle bisector if you already know that the two angles are congruent.


What is the duration of A Game of Two Halves?

The duration of A Game of Two Halves is 1800.0 seconds.


What is the axis of symmetry of a trapeze?

The axis of symmetry of a trapeze, or trapezoid, is a line that divides the shape into two mirror-image halves. For an isosceles trapeze, this axis of symmetry runs vertically through the midpoint of the top and bottom bases. In contrast, a scalene trapeze does not have any axis of symmetry.


It appears from the name of the HL Theorem that you actually need to know that only two parts of two triangles are congruent in order to prove two triangles congruent Is this the case?

No. You can know all three angles of both and all you can say is that the triangles are similar. Or with any pair of congruent sides you can have an acute angle between them or an obtuse angle.


What is the donkey theorem?

When trying to prove two triangles congruent, you can use SSS, SAS, ASA, AAS, HL, and HA patterns. However, the pattern A S S doesn't work. Instead of spelling or saying this word in class, you can refer to it as "the donkey theorem". You can look at the pattern in the two triangles and say "these two triangles are not congruent because of the donkey theorem." You CANNOT prove triangles incongruent with 'the donkey theorem', nor can you prove them congruent. It's mostly sort of a joke, you could say, but it's never useful. The reason is that if the two triangles ARE congruent, then of course there will be an unincluded congruent angle as well as two congruent sides. The theorem doesn't do anything left, right, forward or backward. It's not even really a theorem. :P

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