`Measurement of Objects Using Similar Triangles in The PlaneJohn Gabrielson                Chicago H. S. for Agri. Science                               3807 W. 111th Street                                Chicago IL  60655                               (312)535-2500Objectives:The students in the high school geometry class will apply the use of similar triangles to a sight tool in order to measure the distance between, or heightof large objects such as buildings or trees.   Materials Needed:(Dimensions used can be adjusted for own use)1/2 inch plastic tubing cut into 2' length for sight tube1" x 2" x 4' wood base and arm29cm x 33cm cardboard squares30cm string cordWasher weightBolt with wing nut and locking washer Copy of centimeter rulerLong tape measureStrategy:    Construction of this measuring tool involves fastening two 1" x 2" x 4' boards with bolt wing nut and locking washer placed together approximately one inch from the end of both boards.  This will form the one arm and the base of the tool.       The 30cm string cord with a washer weight is attached to upper left hand corner of the 29cm x 33cm card.  This card with weighted cord is attached over the head of the bolt of the measuring tool at the edge of the joined stick.  A sight tube is glued onto the arm above the attached card at the top corner edge of the joined stick.  This forms the top upper corner of the measuring tool.  Leveling the measuring tool will set the position where the weighted cord crosses the bottom of the card in a position exactly even with the position of its attachment to the top corner of the card.  This will help determine where the zero position of the copy of the centimeter ruler should be glued.     An angle of elevation will be formed by looking through the sight tube.  The top of an object observed will form the local point.  This is point b of the triangle.  A line can be imagined across from the eye of the observer to the object observed.  On this object point c can be named.  The eye of the observer forms point a.  A large triangle has been formed by the thought process of connecting the points from the eye of the observer, to the top of the object observed, to the eye level on the object, back to the observer.       A second triangle similar to the above triangle will be formed onto the cardboard card attached to the measuring devise.  When the measuring devise is elevated the cord will move across the centimeter ruler glued at the bottom of the card.  When the cord stops moving, it will provide the measurement of a side.  Label this crossing, point e.  Point d can be named at the top of the  where the cord is attached.  Point f can be named at the bottom corner of the card where the card forms a right triangle.  Segment df will be the side of the card and the other side of the small triangle segment ef will be the measurement along the centimeter ruler.      In order to solve these similar triangles the observers will have to know either the height of the object to find the distance or the distance to the object to find the height.  One then can set up the equality:                        bc  =  ac                                                                   .                ef     dfHaving three knowns, two on the card, and one from the triangle of the object observed, one can solve the problem.       The teacher will use this tool in a lesson to instruct students about similar triangles.  The students can be taught the concept of similar triangles using a proportional growth pattern of triangles.  This can be followed by instructional use of the tool.  The students are then to be brought outside and begin the actual computation of similar triangles by using the measuring tool.Performance Assessment:The students can be evaluated in groups.  Collection of group work will reveal how accurately the measurements were taken.  Correct mathematics can also be checked.  The scores given can then be recorded and individuals will be given a group grade.`