Question

3

nat you ho has cheated on this exam. 1. Let AABN and AA'B'Y by asymptotic triangles. Prove that if LABN 2 ZA'B'Y and AB> ΑΒ , then /BAΩ< ΒA. 2. Let AABC be an ordinary triangle and let D be any point of the interior. Prove that the sum of the angles of AABD is greater than the sum of the angles of AABC. 3. Suppose that two lines & and m have a common perpendicular MN. Let A and B be points on ( such that A M B. Let C and D be points on m such that AC 1 m and BD L m. Prove that if AM > BM, then AC > BD. M. 4. Let AABC be any triangle. Let D be the midpoint of AB and let E be the midpoint of AC. Let G and F be points on DE such that BF and CG are both perpendicular to DE. (a) Prove that BCGF is a Saccheri Quadrilateral. (b) Prove that DE <BC. (Compare this to Lemma 8.1 in Euclidean Geometry.)

Answer 1

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MB e AC Im BD Im SinD = B =) Sin900 BD > 1 = BD = [BD = BNI Sinn - Mesote singon=1 MIN=MQ TAMABM 7 . Again, MN = shma "GAHITARAY(0380T45& BENAR: (0332946777666 GARIA: ( U245020 A to Z -> MNE AND MN = ANIME Now, AC = singoo=1 =) AG: AN 4 BM. Sin M Singo BN = [BM = BN] Again, A = sin M = singo" = 1 LAM= AMI TAM=AN FACT & (BM = BN = BD VAL.P. HU 033) 2000 OBORIOS A ALX ( 2 A i AM > BM => [AC » BD ] (Proved) SITUITARRA T