Elementary Geometry for College Students
6th Edition
ISBN: 9781285195698
Author: Daniel C. Alexander, Geralyn M. Koeberlein
Publisher: Cengage Learning
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Chapter 2.CR, Problem 13CR
To determine
To find:
The values of
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3. Construct a triangle in the Poincare plane with all sides equal to ln(2). (Hint: Use the fact that, the circle with center (0,a) and radius ln(r), r>1 in the Poincaré plane is equal to the point set { (x,y) : x^2+(y-1/2(r+1/r)a)^2=1/4(r-1/r)^2a^2 }
n. g. = neutral geometry
<ABC = angle ABC
\leq = less or equal than
sqrt{x} = square root of x
cLr = the line in the Poincaré plane defined by the equation (x-c)^2+y^2=r^2
1. Find the bisector of the angle <ABC in the Poincaré plane, where A=(0,5), B=(0,3) and C=(2,\sqrt{21})
2. Let l=2L\sqrt{5} and P=(1,2) in the Poincaré plane. Find the uniqe line l' through P such that l' is orthogonal to l.
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- Let A, B and C be three points in neutral geometry, lying on a circle with center D. If D is in the interior of the triangle ABC, then show that m(<ABC) \leq 1/2m(<ADC).arrow_forwardиз Review the deck below and determine its total square footage (add its deck and backsplash square footage together to get the result). Type your answer in the entry box and click Submit. 126 1/2" 5" backsplash A 158" CL 79" B 26" Type your answer here.arrow_forwardIn the graph below triangle I'J'K' is the image of triangle UK after a dilation. 104Y 9 CO 8 7 6 5 I 4 3 2 J -10 -9 -8 -7 -6 -5 -4 -3 -21 1 2 3 4 5 6 7 8 9 10 2 K -3 -4 K' 5 -6 What is the center of dilation? (0.0) (-5. 2) (-8. 11 (9.-3) 6- 10arrow_forward
- Select all that apply. 104 8 6 4 2 U U' -10 -8 -6 4 -2 2 4 6 10 -2 V' W' -4 -6 -8 -10 W V Select 2 correct answerts! The side lengths are equal in measure. The scale factor is 1/5. The figure has been enlarged in size. The center of dilation is (0.0) 8 10 Xarrow_forwardIn the graph below triangle I'J'K' is the image of triangle UK after a dilation. 104Y 9 CO 8 7 6 5 I 4 3 2 J -10 -9 -8 -7 -6 -5 -4 -3 -21 1 2 3 4 5 6 7 8 9 10 2 K -3 -4 K' 5 -6 What is the center of dilation? (0.0) (-5. 2) (-8. 11 (9.-3) 6- 10arrow_forwardQll consider the problem -abu+bou+cu=f., u=0 ondor I prove atu, ul conts. @ if Blu,v) = (b. 14, U) + ((4,0) prove that B244) = ((c- — ob)4;4) ③if c±vbo prove that acuius v. elliptic.arrow_forward
- Q3: Define the linear functional J: H₁(2) R by ¡(v) = a(v, v) - L(v) Л Let u be the unique weak solution to a(u,v) = L(v) in H(2) and suppose that a(...) is a symmetric bilinear form on H(2) prove that 1- u is minimizer. 2- u is unique. 3- The minimizer J(u) can be rewritten under 1(u) = u Au-ub, algebraic form 1 2 Where A, b are repictively the stiffence matrix and the load vector Q4: A) Answer 1- show that the solution to -Au = f in A, u = 0 on a satisfies the stability Vullfll and show that ||V(u u)||||||2 - ||vu||2 2- Prove that Where lu-ul Chuz - !ull = a(u, u) = Vu. Vu dx + fu. uds B) Consider the bilinea forta Л a(u, v) = (Au, Av) (Vu, Vv + (Vu, v) + (u,v) Show that a(u, v) continues and V- elliptic on H(2)arrow_forward7) In the diagram below of quadrilateral ABCD, E and F are points on AB and CD respectively, BE=DF, and AE = CF. Which conclusion can be proven? A 1) ED = FB 2) AB CD 3) ZA = ZC 4) ZAED/CFB E B D 0arrow_forward1) In parallelogram EFGH, diagonals EG and FH intersect at point I such that EI = 2x - 2 and EG = 3x + 11. Which of the following is the length of GH? a) 15 b) 28 c) 32 d) 56arrow_forward
- 5) Which of the following are properties of all squares: 1. Congruent diagonals 2. Perpendicular diagonals 3. Diagonals that bisect vertex angles a) 1 and 2 only b) 1 and 3 only c) 2 and 3 only d) 1, 2, and 3arrow_forward6) In an isosceles trapezoid HIJK it is known that IJ || KH. Which of the following must also be true? a) IJ = KH b) HIJK c) HIJK d) IJ KHarrow_forward4) When rectangle JKLM is plotted in the coordinate plane side JK has a slope equal to 3. What must be the slope of side MJ? a) 3/3 b) e 35 53 32 d) - 5arrow_forward
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