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From Chapter 6:
Assignment 4, 2015 Due November 4
Problem 6.2 C (the converse of ITT) If a triangle has two angles congruent, then two sides
are congruent
plus the following corollary to this proof : In an isosceles traingle, the right bisector of the
base is the angle bisector of the opposite angle.
This is ‘like’ the corollary (b) to our Proof of ITT. Do this on Plane and on the Sphere
without restrictions on the size of the ‘triangles’.
Problem 6.5: Prove Angle Side Angle on Plane and Sphere. Give a suitable definition of
which triangles this one proof works for, on the plane and the sphere.
We have done SAS in class, so you are now doing this analog. Some questions come up
about which shapes (which ‘triangles’) this applies to – so be clear when you finish whether
you had to add restrictions, which examples made restrictions necessary, etc.
In the proofs, use multiple-diagrams and consider how to use an incomplete diagram to
avoid mistakes in the proofs.
Question / Reflection: Include a few questions you now have (something related to a
possible final project could be included) and indicate how you might go about answering
the question, yourself. (Simply giving the question. without context or further reflection is
not enough.)
Added Bonus Question.
In class we showed a proof that the angle bisectors of three interior angles meet in a point
(plane and sphere). This point is the incenter (where a circle can be created touching all
three sides). This is an extension:
Show that there is a circle that touches the triangle from outside – touching one side in its
interior, and two sides in their extensions. This is an excenter. Do this proof on both the
plane and the sphere.