Problem 2 Consider the triangle ABC in the picture below. AB707 (a) Use linear algebra to...
Given a triangle ABC, let l_1 be the angle bisector of <A and let l_2 be the perpendicular bisector of line BC. Assuming AB > AC, show that l_1 intersection l_2 is not in triangle ABC Excuse l_2 is the perpendicular bisector of line BC hence the right angle. The questions is to show a step by step proof that when l_1 abd l_2 intersect, it will be outside of the given triangle. Given a triangle ABe, let Libe the...
c) Consider the figure below. It is given that A ABC is a 30-60° right triangle, A DEF is an isosceles triangle with DF = EF, DE | AC, ZDEF = 65°, ZDIL = 38.2, and ZIK) = 31'. Find all angles in the figure and mark them on the figure. Clearly show all your work B D G E A
Points W and X are chosen on the side AB of triangle ABC and points Y and Z are chosen on side AC. Suppose that cr(A,W,X,B)=cr(A,Y,Z,C) and that WY is parallel to XZ. Prove that XZ is parallel to BC. Hint: let T be the point where the parallel to XZ through B meets line AC. Note that neither a nor Y can lie on segment TC and use excercise 3C.2 to show that T is C. cr=cross ratio
Do not use I=delta/S!!! Use law of cosines Here is the question: Let r be the radius of the incircle of triangle ABC on the unit sphere S. If all the angles in triangle ABC are right angles, what is the exact value of cos r? Note in spherical geometry the angles sum is>180 Using below picture (this is what we are given), we should know angle b and the angle at the perpendicular. If we find the length on...
2. Consider a triangle ABC. Let M denote the midpoint of side AC. If BM - AM, show that angle B is a right angle. (10 points)
The picture below shows a triangle A BC. s ed KS ed KS ed ed The point Dis of the way along the line AB. It is not plotted accurately in this picture! The point E is half way along CD. The following vectors are also defined AB = AC = (-) Answered 6 marks a) Answered Calculate the following vectors. 6 marks Answered BC = 7 marks Answered AD = 7 marks Partially answered 2 marks Answered DE =...
1. Consider the isosceles triangle ABC, with AB = AC, and BAC = 20. Choose points E, D on the sides AB, AC, respectively, so that ZCBD = 60', and BCE = 50'. We will find LEDB. (i) Bring the parallel DF to BC, with F on AB. Connect points and F. and let K be the intersection of BD and CF. Show that DFBC is an isosceles trapezium. Mark all its angles. (ii) What type of triangles are BKC...
hint for d): consider a point D such that M is the midpoint of CD. Which segments are congruent here? Do you see a triangle with all three side lengts given. Could you please write some instructions on the side so I know how to follow your solution? 5. Given a triangle ABC, let M be the midpoint of the segment AB. The segment CM is called the median of the triangle. Let T be the point on the line...
Matrix Methods/Linear Algebra: Please show all work and justify the answer! 1. Consider the following matrices. [-1:] 1 2 2 0 A= -10.B=3-4 and C= 3 4 5 Compute each of the following, if it is defined. If an expression is undefined, explain why. (a) (4 points) A+B (b) (4 points) 2B (e) (4 points) AC (d) (4 points) CB
28 Consider (O:OAOB) an orthonormal system in space. Let G be the center of gravity of triangle ABC. 1° Calculate the coordinates of G 2°Consider the points A' (2 ;0:0) ,B, (0:2:0) and C" (0:0,3). a) Verify that these three points define a plane. b) Write a system of parametric equations of the plane (A'BC'). 3 Write a system of parametric equations of line (AC). 4° Verify that K (4:0-3) is the trace of the line (AC) with the plane...