Parallel Bars Across Two Rods

In the picture

1. 1The shared point: both triangles have it as their tip
2. 2The short parallel bar: it closes the small triangle
3. 3The long parallel bar: it closes the big triangle, a scaled copy of the small one
4. 4A piece of the green rod: it is in the same ratio to the rest of its rod as the matching piece of the blue rod

Examples

• Measuring a tree’s height by comparing its shadow with the shadow of a stick of known length
• A projector: the image on a farther screen is larger but has exactly the same shape

Quiz: Parallel Bars Across Two Rods (Age 14)

1. 1

   When two lines cut across two rays that start at the same point, what must be true for the cut pieces to be in proportion?

   • The two cutting lines must be the same length
   • The two cutting lines must be parallel
   • The two rays must be the same length
2. 2

   Two parallel lines cut two rays from one point. One side of the small triangle is half as long as the matching side of the big triangle. What can you say about another matching pair of sides?

   • The small side is shorter by the same number of centimetres
   • It could be any fraction, depending on the angle at the shared point
   • The small side is also half of its matching big side
3. 3

   How is the small triangle related to the big triangle when parallel lines cut two rays from one point?

   • They have the same shape, and the big one is a scaled-up copy of the small one
   • They have the same shape only if the two rays are the same length
   • They have the same area but different shapes

The answers, each with its explanation, are in the app. This quiz is free there while the lesson is in the free week.