2. Consider a triangle ABC. Let M denote the midpoint of side AC. If BM -...
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...
Let ABC be a right triangle with hypotenuse AC. Let BD be the altitude to the hypotenuse. Let BE be the angle bisector of angle DBC, and AF be the angle bisector of angle DAB. Prove EB is perpendicular to FA.
△ABC is a right triangle with right angle C. Side AC is 6 units longer than side BC . If the hypotenuse has length 52–√ units, find the length of AC. courseware-Google Chrome a https://www.casa.uh.edu /Root/Pages/CW aspx?id 643857CE-8CB9-4B21-AC4B-1AD73C216A8D CourseWare Quiz 18 Howard, Calvin d) V10 e)V30 f None of the above CLOCK Start 11/7/2018 11:42:20 AM Taken 00:02:02 NAVIGATION Question 5 Q 1 Q2 Q3 Q4 Your answer is INCORRECT [100 Q 6 ABC is a right triangle with right...
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...
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...
Let traingle ABC have midpoint B' on AC, C' midpoint of AB and G be centroid. If AC=5, AB=5, and CC'=6 find BC.
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
Question B Diagram NOT accurately drawn 2 2b APB is a triangle. N is a point on AP. AB- a AN 2b NP-b (a) Find the vector PB, in terms of a and b. 3b 10 B is the midpoint of AC. M is the midpoint of PB. *(b) Show that NMC is a straight line. Diagram NOT accurately drawn 2 2b APB is a triangle. N is a point on AP. AB- a AN 2b NP-b (a) Find the...
Problem 2. [25 pts) Side AB of the square ABCD is extended to P, A - B - P, so that BP 2 AB. With M the midpoint of DC, BM is drawn meeting AC at Q. PQ meets BC at R. Using Menelaus' theorem find the ratio R. P C M Problem 2. [25 pts) Side AB of the square ABCD is extended to P, A - B - P, so that BP 2 AB. With M the midpoint...
Additional Problem: Suppose that AABC has sides AB 31,AC 35, and M is the midpoint of BC. The goal is to obtain the inequality 2 < x <33, where x AM. Construct the auxiliary lines shown, with M the midpoint of AE a. Find y-CE. Then show that 2x-AE 66. b. Show that AM (66)-33 C. Show that 2 < x < 33. (Hint: Use the Triangle Inequality in AEC. 31 35