**NOTE**: Please WAIT while the applet below loads.

**Exploration:**

1) Start with any Δ*ABC* and an arbitrary point *D* on *AB*. From *D* construct a line parallel to *AC*, to intersect *BC* at *E*.

2) Click on the **+** buttons on the top right of the sketch below in sequence to construct *EF* // *BA*, *FG* // *BC*, etc.

**Conjecture:**

1) What do you notice when you draw the line through *I* parallel to *CB*?

2) Click on the last **+** button below the sketch to show the perimeters of *ABC* and *DEFGHI*. What do you notice?

3) Make conjectures regarding your observations in 1) and 2). Then carefully CHECK your conjectures by dragging *D*, or dragging any of the vertices *A*, *B* or *C*.

Perimeter of inscribed parallel-hexagon

**Explanation (proof):**

Can you *explain why* (prove) your two conjectures above are true?

**Explore more:**

1) Can you generalize further to the perimeters of polygons inscribed similarly for quadrilaterals, pentagons, etc.? Explore!

2) Explore the relationship between the *area* of the inscribed hexagon and that of the triangle, as well as the areas of the analogous cases for quadrilaterals, pentagons, etc. Go here for some interactive sketches: *areas of some inscribed polygons*.

*Back to "Dynamic Geometry Sketches"*

*Back to "Student Explorations"*

Created by Michael de Villiers, 24 February 2016.