Modeling Prompt

Students will not have seen how to trisect a line segment, which they will need to do in order to construct \(AC\). They can measure first to see where the points that trisect the line should go. Instructions for trisecting a line segment can be found online. There are many ways of doing it, and some are easier than others, so if students find the instructions themselves they should be encouraged to compare several methods before deciding which one they prefer. If students try different methods, it could be beneficial to invite selected students to show the class what they did. The other steps for constructing the flag should be familiar. Having access to geometry software can streamline the construction process.

If students have trouble getting started with finding the angles, they can try giving \(AB\) a specific value and calculating the other side lengths.

Once students have completed the task, invite them to share the flags they chose and show how they adapted them to fit on the triangular banner.

The constitution of Nepal includes instructions for constructing the flag. Here are the instructions:

Step 1: Draw a line \(AB\) of the required length. \(AB\) will be the bottom edge of the flag.
Step 2: Draw a line \(AC\) perpendicular to \(AB\) so that the length of \(AC\) is \(\frac43\) the length of \(AB\).
Step 3: Mark the point \(D\) on the line \(AC\) so that \(AD\) is the same length as \(AB\). Then join the points \(D\) and \(B\) with a straight line.
Step 4: Mark the point \(E\) on the line \(BD\) so that \(BE\) is the same length as \(AB\).
Step 5: Draw a line \(FG\) that goes through \(E\), is parallel to \(AB\), and is the same length as \(AB\). \(F\) should be on the line \(AC\).
Step 6: Join the points \(C\) and \(G\) with a straight line.

1. 1. Construct the flag according to the instructions. You can make it any size you want.

   2. Find the measure of each of the angles in the flag.

2. Imagine that there will be a parade featuring the flag of Nepal. For the parade there will be small flags and large flags. Decide what the sizes of each type of flag should be.

   1. How much material would you need to make each type of flag?

   2. If you made the border of the flags by sewing a ribbon along the edge, how long would the ribbon have to be for each type of flag?

3. Imagine that there will be a parade featuring a flag that is meaningful to you. (Choose a flag or design your own.) At the parade there will be small flags, large flags, and triangular banners like this:

   

   

   1. How will you adapt your flag to fit on the triangular shape?

   2. How much material of each color will you need for each kind of flag?

Students who want an extra challenge can find the areas and perimeters of both the small and large flag in the second question, and then compare the areas to see the effect of the scale factor. The relationship between scaling lengths and scaling areas will be a topic in the next unit, so students do not need to have a full understanding of it at this time, but this is a good opportunity to preview the concept.

Another opportunity for an extra challenge is to try describing the exact ratios between the side lengths using radicals. An especially interesting thing students may notice is that the ratio between \(AF\) and \(AD\) is the same as the ratio between \(AD\) and \(BD\), \(\tfrac{1}{\sqrt2}\).

Having access to geometry software can help students visualize the shapes they are working with.

Once students have completed the task, invite them to share the flags they chose and show how they adapted them to fit on the triangular banner.

The constitution of Nepal includes instructions for constructing the flag. Here are the instructions:

Step 1: Draw a line \(AB\) of the required length. \(AB\) will be the bottom edge of the flag.
Step 2: Draw a line \(AC\) perpendicular to \(AB\) so that the length of \(AC\) is \(\frac43\) the length of \(AB\).
Step 3: Mark the point \(D\) on the line \(AC\) so that \(AD\) is the same length as \(AB\). Then join the points \(D\) and \(B\) with a straight line.
Step 4: Mark the point \(E\) on the line \(BD\) so that \(BE\) is the same length as \(AB\).
Step 5: Draw a line \(FG\) that goes through \(E\), is parallel to \(AB\), and is the same length as \(AB\). \(F\) should be on the line \(AC\).
Step 6: Join the points \(C\) and \(G\) with a straight line.

1. Clare is constructing the flag and she starts with \(AB\) of length 6 inches. Here is her finished flag shape. Use the instructions to fill in as many lengths and angles as you can.

   

   

2. Imagine that there will be a parade featuring the flag of Nepal. For the parade there will be small flags and large flags. For one of those types, decide how big it should be.

   1. How much material would you need to make the flag?

   2. If you made the border of the flag by sewing a ribbon along the edge, how long would the ribbon have to be?

3. Imagine that there will be a parade featuring a flag that is meaningful to you. (Choose a flag or design your own.) At the parade there will be rectangular flags and triangular banners like this:

   

   

   1. How will you adapt your flag to fit on the triangular shape?

   2. How much material of each color will you need for each kind of flag?