P1 Using the glossary for the Poincare disk model translate

P-1. Using the glossary for the Poincare disk model, translate the following throrems in hyperbolic geometry into theorems in Euclidea Geometry: a. If two triangles are similar, then they are congruent. b. If two lines are divergently paralled, then they ahve a common perpendicular and the latter is unique. c. The fourth angle of a Lambert quadrilateral is acute. Please explain your work. Thank you!

on which lies a segment P congruent with both PQ and pro in the sense of (1). Justify (11 by drawing the diagram in the Klein model and then applying Lemma 7.5 and Theorem Blumenthal and Menger, 1970, p. 220). P-Exercises P-1. Using the glossary for the Poincaré disk model, translate the fol lowing theorems in hyperbolic geometry into theorems in Eu- clidean geometry: (a) If two triangles are similar, then they are congruent. (b) If two lines are divergently parallel, then they have a com- mon perpendicular and the latter is unique. (c) The fourth angle of a Lambert quadrilateral is acute. P-2. State and prove the analogue of Proposition 7.6 when o lies in- side 6 and the power p of o with respect to is negative. P-3. Let be a circle with center C and a a circle not through C hav- ing center A. Let A\' be the inverse of A in and let circle a\' be the image of a under inversion in 5. Prove that A\' is the inverse of c in a\' and hence that A\' is not the center of a\'. (Hint: Show that any circle B through A\' and c is orthogonal to a\' by ob serving that the image B\' of B under inversion in 6 is a line o

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