Math 445 Class, March 2

Question 1A:

The excess of a triangle ABC is defined to be (angle A + angle B + angle C – 180), where the angles are measured in degrees.

In this figure, compute the excesses of the 3 triangles ABC, ACD and ADB and find a relationship between them.

Question 1B:

The defect of a triangle ABC is defined to be (180 - angle A - angle B - angle C), where the angles are measured in degrees.

In this figure, compute the defects of the 3 triangles ABC, ACD and ADB and find a relationship between them. (This is supposed to be very easy, so look before jumping into a long computation.)

Question 2:

The triangle below is a P-triangle (the point A is the center of the disk). What can you say about the sign of the excess and the defect of this triangle? Explain.

Will the same result about the signs be true of any triangle in the P-model? Why?