_____________________________________________________ River Technique #2. Another technique involves trying to lay out a square with one side being the distance to be measured, d, and another side along the accessible shore. The square is laid out by a person walking from point A along the shore at right angles to the width of the river until the angle over to the inaccessible point, B, is estimated to be 45 degrees. The two sides of the square have the same length and, since you know how many paces is the side along the shore, you know that the distance across the river is the same length. 1) Surveyors are brought in to find the length of a swimming race across part of a lake from A to B. They set up a tripod at point C. They also located the midpoints of AC and BC. When they connected these two points they found the distance to be 48 meters. What other distances are needed to find the length of the swim across the water? 2) The isosceles triangle below is a diagram of the wall on the main building of the Rock and Roll Hall of Fame. The base is 229 feet 6 inches. Each side of the triangle is broken up into four congruent parts buy the diagonal struts. What is the length of the grey horizontal beam AB? _____________________________________________________ _____________________________________________________ 3) There is a kayak race across the lake below from point A to point B. Surveyors are brought in to find out if the length of the race is long enough to qualify for a record. They set up a tripod at point C. Complete this diagram and word problem with just enough information for your fellow student to work out the distance of the race. Exit Slip Describe the mid-segment of a triangle. AC is 42 cm. and BC is 38 cm. If D and E are the midpoints of AC and AB respectively, what is the length of DC? What is the length of the mid-segment? Congruent and Similar Triangles Name: ___________________________ Date : _____________ PART I I need to measure the distance across a river, but I cannot stretch my tape measure across the water. I am using my knowledge of similar figures to help me solve this problem. There are two trees on the bank of the river on the opposite side. I rowed my boat across and measured the distance between these two trees. Now I set up three stakes in the ground which form a triangle. When I stand at point A, the line of sight from me to each tree passes directly over both stake C and stake B. Now I am measuring two sides of the triangle formed by the stakes. How can I use this information to find the distance across the river? PART II The South Bronx Look at the map of an area in the South Bronx. All of the streets which run from East to West are parallel to each other and are exactly 50 yards apart if I am walking along any of the following avenues: Alexander Ave., Willis Ave., Brook Ave. or St. Anns Ave These avenues all make angles of 70o with each of the streets. Alexander Ave., Willis Ave., Brook Ave. and St. Anns Ave. all run from North to South and they are also parallel to each other and they are exactly 396 yards apart. Third Ave. and Fourth Ave. as you can see on the map is not parallel to the avenues mentioned above but they are parallel to each other. Third and Fourth Avenues make angles of 50o with each of the streets. 1) What angle does Third Ave. make with Willis Ave. ? _____________________________________________________ _____________________________________________________ _____________________________________________________ 2) If I walk west to east along any of the streets what is the distance from Third Avenue to Fourth Avenue ? _____________________________________________________ _____________________________________________________ 3) Can you name at least three pairs of congruent triangle ? You must draw the triangles below and label the streets/avenues and tell how you know they are congruent. 4) What is the distance between Third Ave. and Willis Ave. if I am walking on 138th Street ? _____________________________________________________ _____________________________________________________ _____________________________________________________ 5) I am racing my friend from Third Ave. to Willis Ave. I am running on 145th Street and my friend is running on 144th Street ? Who has to run further and how much further is it? _____________________________________________________ _____________________________________________________ 6) What is the distance between Third Ave. and alexander Ave. if I am walking on 140th Street ? _____________________________________________________ _____________________________________________________ 7) What is the ratio of the areas of the land surrounded by Brook Ave., St Anns Ave., 147th St. and 148th St. compared to the land surrounded by Alexander Ave., St. Anns Ave., 139th St. and 143rd St. ? _____________________________________________________ _____________________________________________________