Ms. Wong, Period 4 Geometry Unit 4 Triangles Take-Home Exam

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1 Ms. Wong, Period 4 Geometry Unit 4 Triangles Take-Home Exam Note: As always, each question must accompany work that indicates how you obtained your answer. If you show your work on a separate sheet of paper, be sure to put your name in the top RIGHT HAND corner and that you NUMBER the problem for which you are showing work. **NO COLLABORATION IS ALLOWED ON THIS ASSIGNMENT. If there is reason to believe you did not complete this assignment faithfully or there is evidence of academic dishonesty in your submission, you will receive a score of zero. You may, however, use your class notes, your homework assignments, our class website ( and the internet to help you through the problems. Due: Wednesday, April 8 th, at 1:05pm Your submission must be hard-copy and submitted by the date and time listed above, otherwise it will not be accepted; NO EXCEPTIONS! Questions? Comments? Concerns? Please address them with Ms. Wong at Shellee.Wong@qacps.org ***NO questions will be answered via on Tuesday, April 7 th, so PLEASE do NOT wait until Tuesday to begin the assignment.***

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3 Name Date Unit 4 Assessment: Triangles Ms. Wong Pd 4 Geometry STUDENTS MUST SHOW ALL WORK TO RECEIVE ANY PARTIAL CREDIT. Work presented on a separate sheet of paper must be labeled with student s name and each problem must be clearly numbered. A correct multiple choice response with no work shown will be awarded with AT MOST 1 point. (3 points each) 1. Three sidewalks cross near the middle of City Park, forming a triangular region. Levi donated money to the city to create a fountain in memory of his father. He wants the fountain to be located at a place that is equidistant from the three sidewalks. Which point of concurrency should be located? A. Orthocenter B. Centroid C. Circumcenter D. Incenter 2. Which of the points of concurrency is illustrated in the diagram below? 1. A. Orthocenter B. Centroid C. Circumcenter D. Incenter Three docks are located on opposing sides of a river, as shown in the diagram below. Using the information provided, what is the measure of DOC? A. 17 o B. 53 o C. 127 o D. 197 o In JKL, m J = 104 o, m K = a o, m L = x o. Find the measure of L. A. L = (76 a) o B. L = (76 + a) o C. L = (104 a) o D. L = (104 + a) o 4.

4 5. Solve for the missing angle. A. 70 o B. 80 o C. 120 o D. 130 o 5. For 6-9, select the choice that represents the line/segment/ray indicated in the accompanying diagram

5 10. An isosceles triangle can be defined as a triangle with at least two congruent sides. Using this definition, what other type of triangle could be described as isosceles? Explain. (3 pts) 11. ABC is an isosceles triangle with vertex angle B, AB = (5x-28) inches, AC = (x + 5) inches, and BC = (2x + 11) inches. Determine the length of the base of the triangle. (6 pts) 12. ABC is shown below, with A(0,0), B(2,2), and C(4,1). Find the coordinates of the location of the centroid. ( 5 points) 13. The bottom of a 12-foot straight ladder is set into the ground 2 6 feet away from a wall. When the top of the ladder is leaned against the wall, what is the distance above the ground it will reach? (5 points) 14. A 60-foot cable stretched from the top of a pole to an anchor on the ground. It is anchored on the ground 19 feet away from the base of the pole. How tall is the pole? (5 points)

6 15. In the following diagram, O is the centroid of triangle PAT. (5 points total) 16. A new emergency response center is to be placed in a city so that it is equidistant to a hospital, an elderly care facility, and an elementary school. You are in charge of determining where to place the new facility. (7 points) a. Determine the point of concurrency that helps you to locate the response center. b. Explain how you would use constructions (what would you do with a compass and straightedge) to locate the center give the step by step instructions.

7 17. Use the accompanying diagram. a. What is the measure of angle BAQ? (5 points) b. What is the measure of angle BCA? (5 points) 18. While looking through a trunk in your grandmother s attic, you find a map with a note leading to a treasure on a tropical island. You determine that the treasure is buried in a location so that it makes a triangle with a tree and a cave on the island. The distance from the treasure to both the tree and the cave is the same as the distance from the tree to the cave. Where on the island should you look for the treasure? Explain how you determined where to look. You may want to explain what lines/point of concurrency was used to locate the point. (3 points) 19. What is the length of the longest diagonal in a rectangular prism (NOT a rectangle, BE CAREFUL!) that is 10 in x 6 in x 2 in? (6 points)

8 20. Use the accompanying diagram. a. Find the value of x. (5 points) b. Find the measure of angle 2. (2 points) 21. Use the accompanying diagram. Solve for x. (5 points) 22. Use the accompanying diagram. a. Find the value of x. (5 points) b. Find the measure of angle 2. (2 points)

9 Bonus Question #1: Solve for x. (5 points) Bonus Question #2:Solve for x. (5 points)