Student Page - Homework
Activity 5b Geometry, Ratios, and Similar Triangles

Practice geometry of similar triangles and calculating ratios.

Use a ruler to draw two intersecting lines.  Either fold the paper lengthwise to bisect the resulting X or draw a line through the center.  Now, on one side of the X, draw a perpendicular line.  Measure the distance from the center of  the X to the perpendicular line.  Measure the perpendicular line between both axes of the X.  Draw another perpendicular line.  Repeat the measurements: horizontal line from the center to the second perpendicular line; perpendicular line between the axes.  Find the ratios of the lines from the center of the X to each perpendicular line.  Next find the ratio of the perpendicular lines.  

What did you find out about the ratios?

Try this again with another drawing of an X that looks wider or slimmer.

What did you find out about the ratios?

Note:  This drawing could represent light going through a pinhole as in a pinhole camera.  In the case of a pinhole camera the image forms at any distance from the pinhole.  A telescope is different in several ways.   In a telescope the light is collected over a much larger area than a pinhole, the mirror or lens focuses the light onto an image plane,  the image plane is at a very specific distance from the lens or mirror which is dependent on the curvature of its surface.   Nevertheless, comparing focal distances and image sizes results in proportional relationships.