EDUC 272 Final, Spring 2009

Name: EDUC 272 Final Exam Spring 2008-2009 Geometry Weight: 30% Exercise 1: A CB radio station C is located 3 mi from the interstate highway h. The station has a range of 6.1 mi in all directions from the station. If the interstate (connecting between two or more states) is along a straight line, how many miles of highway are in the range of this station? Explain your answer. (4 pts) Exercise 2: Consider the AABC with vertices having coordinates A(2, 2), B(5, 2) and C(2, 6). What type of triangle is AABC? Explain your answer. (4 pts) Exercise 3: In AABC, line (DE) is parallel to line (AB), and line (DF) is parallel to line (AC). If m(<C)=70° and m(<B)=45°, find the measure of the angles labeled 1, 2, 3, 4 and 5. (4pts) c [> Exercise 4: These conjectures were made by students in a school. Determine whether you agree or disagree and write an argument to support your viewpoint. (2 % pts) a. All triangles with the same area are congruent. b. Right triangles cannot be scalene. c. Triangles with equal areas have equal perimeters d. The area of any triangle is 4 the area of the rectangle with the same base and height Exercise 5: use slope to determine if there is a single line through the points with coordinates (4, 2), (0, -1), and (7, -5). Explain your reasoning. (2 pts) Exercise 6: If the area of a rectangle remains constant but its perimeter has increased, how has the shape of the rectangle changed? Explain. (2 pts) Exercise 7: Given AABC with parallel lines dividing segment AB into three congruent segments as shown, how does the area of ABDE compare with area of DEFG? Explain. (2 pts) Exercise 8: Given the following figure. Find x. Explain. (2 pts) 50m Exercise 9: a. Draw a traversable network that has more than four vertices. Indicate an appropriate path through it labeling the starting and stopping points. b. Is your network above an Euler Circuit? Explain why or why not. c. Using a fewest possible number of vertices and arcs, draw a network that is not traversable. (3 % pts) Exercise 10: In triangle ABC, a square has been inscribed as shown. The lengths of the sides of A ABC are 3, 4 and 5 as shown. Find the length of a side of the square. (2 pts) Exercise 11: In the following figure, quadrilateral ABCD is a parallelogram and P is any point on [AC]. Prove that the area of ABCP is equal to the area of ADPC. (2 pts) Good luck