Investigating Geometry: Similarity

Henrico County Public Schools

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May 2006

Lesson 5-3: Identifying Similar Triangles



You are on the southside of a river and wish to find the distance across a river. You can create a model using similar triangles to find a distance that can’t be measured directly.

Objective:

SOL G.7: The student, given information in the form of a figure or statement, will prove two triangles are similar, using algebraic and coordinate methods as well as deductive proofs.

 Applet Directions 1 Close 
  1. Locate yourself directly across the river from the Tree and construct a perpendicular line to the riverbank through the Tree

  2. Construct a point, A, where the perpendicular line intersects the riverbank.

  3. Construct 2 more points along the same riverbank and side of the perpendicular.

  4. Use the tool to name the points A, B, C.

  5. Construct a perpendicular line to the bank through point C.

  6. Construct a ray from the Tree through B.
 Applet Directions 2 Close 
  1. Place a point at the intersection of the ray and perpendicular line and label it D.

  2. Move points B, or C to view how the model changes.

  3. The distance from the Tree to A is what you wish to find. Before you measure, AB, BC, and CD, write a proportion in terms of these four lengths.

  4. To measure, first click on the icon, then the segment icon . Next click on the endpoints of the segments.

  Hands-On Activities Close 
  1. Copious Amounts

  Other Web Sites web Close 
  1. Glencoe: On Line Quiz
 Puzzle & Problems tangram Close 

At 4:00 PM, a tower casts a shadow 24 feet long. A stop-sign pole nearby casts a shadow 8 feet long. If the stop-sign pole is 9 feet tall, how tall is the tower? Explain your reasoning.