(Be prepared to answer these questions in class, either orally or in writing.)
Reading, Sved 61-66.
The defect of a triangle
Define the defect of a triangle ABC is an angle measure = straight angle
- angle sum = 180 - angle A - angle B - angle C (this is the defect measured
in degrees).
A triangle is defective if its defect is > 0.
In Euclidean geometry, what is the defect of any triangle?
In Spherical geometry, what can you say about the defect of a triangle?
In the geometry described by Sved, the defect is always 0 or >0. Is this
explained or just asserted in these pages?
Defect Addition
Given a triangle ABC and a point D on segment BC, explain why
defect ABC = defect ABD + defect ADC
In the case above, if ABD is defective (in the plane described in Sved),
explain why ABC is also defective.
One defective triangle is enough to cause big trouble
Why is it that a geometry with a single defective triangle cannot have a
big rectangle. (Sved p. 66).
In other words, if a small, defective right triangle occupies a corner of
a big quadrilateral as in Sved, p. 66, why do we know the big quadrilateral
cannot be a rectangle?