311 – HW 8

April 23, 2015

HW 8 is due Tuesday, April 28, at the beginning of lecture.

Work in hyperbolic geometry. Given a triangle \triangle ABC, recall that its Saccheri quadrilateral \Box ABB'A' based at \overleftrightarrow{AB} is defined as follows: Let M be the midpoint of \overline{AC} and N be the midpoint of \overline{CB}. Let A',B' be the feet of the perpendiculars from A and B to MN, respectively.

Continuing with the same notation, suppose now that G is an arbitrary point on \overleftrightarrow{MN}, and let H be a point on the ray \overrightarrow{AG} with GH=AG. Show that \Box ABB'A' is also the Saccheri quadrilateral of \triangle ABH based at \overleftrightarrow{AB}.