1. Geometry-Part 5

2. You can use similar triangles to approximate the width of a river
You can use similar triangles to approximate the width of a river. All you would need is four stakes. The diagram is a top view of the situation.
-Start by selecting a place for point A on one side of the river. A tree or large rock will work.
-Place a stake at point B, directly across the river from point A.
-Walk 20 equal paces from B parallel to the river to mark point C. Then walk another 10 equal paces from point C to mark point D. Place stakes at C and D.
-From D, walk away from the river along a line that is parallel to AB. When points A and C line up, you are at point E. You walked 24 paces from D to E. Place a stake at point E.

3. Name two similar triangles. Why are the two triangles similar
Name two similar triangles. Why are the two triangles similar? Use the triangles in the diagram to find the width of the river.

4. The drawing represents a plane taking off
The drawing represents a plane taking off. At this moment, it is 1,000 m from the point of takeoff, as measured along the ground, and it is 240 m above the ground.

5. Sketch the situation and label the distances that you know
Sketch the situation and label the distances that you know. On your sketch, extend the plane’s takeoff line of flight to a point that is 2500 m from takeoff, as measured along the ground. Draw in the new height from the plane to the ground, and label your diagram with the new information. Identify two triangles in your picture. Are they similar? Explain how you know. When the plane is 2,500 m from the point of takeoff, what is the height? When the plane reaches an altitude of 1,000 m, what is its distance (measured along the ground) from the point of takeoff?