# Building Polygons (Part 2)

Warmup

At a park, the slide is 5 meters east of the swings. Lin is standing 3 meters away from the slide. Draw a diagram of the situation including a place where Lin could be.

(1.) How far away from the swings is Lin in your diagram?

(2.) Where are some other places Lin could be?

Activity #1

Constructing Triangles.

• Build as many different triangles as you can that have one side length of 5 inches and one of 4 inches.
• Record the side lengths of each triangle you build.

(1.) Are there any other lengths that could be used for the third side of the triangle but aren’t values of the sliders?

(2.) Are there any lengths that are values of the sliders but could not be used as the third side of the triangle?

(3.) Assuming you had access to strips of any length, and you used the 9-inch and 5-inch strips as the first two sides, complete the sentences:

(a.) The third side can’t be ________ inches or longer.

(b.) The third side can’t be ________ inches or shorter.

Activity #2

Drawing a Triangle with Given Side Lengths.

We’ll explore a method for drawing a triangle that has three specific side lengths. Use the applet to answer the questions below.

Follow these instructions to mark the possible endpoints of one side:

For now, ignore segment A C , the 3-inch side length on the left side. Let segment B D be the 3-unit side length on the right side.

• Right-click on point D, check Trace On.  ​
• Rotate the point, drawing all the places where a 3-inch side could end and answer the question (1) below.
• Use your drawing to create two unique triangles, each with a base of length 4 inches and a side of length 3 inches.  Use a different color to draw each triangle.
• Repeat the previous instructions, letting segment A C  be the 3-unit side length.
• Using a third color, draw a point where the two traces intersect. Using this third color, draw a triangle with side lengths of 4 inches, 3 inches, and 3 inches.  Answer question (2) below.

(1.) What shape have you drawn while moving  B D around?  Why?  Which tool in your geometry toolkit can do something similiar?

(2.) What do you notice?

Challenge #1

In the diagram, the length of segment AB is 10 units and the radius of the circle centered at A is 4 units. Use this to create two unique triangles, each with a side of length 10 and a side of length 4. Label the sides that have length 10 and 4.

Challenge #2

Here are two patterns made using identical rhombuses. Without using a protractor, determine the value of a and b. Explain or show your reasoning.

Quiz Time