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

From each vertex of Δ*ABC*, draw an *equi-inclined* line to form an *equal angle* with the opposite side. What do you notice about the angles of the formed Δ*HIG* in relation to those of Δ*ABC*? Explore more by dragging some of the points.

Equi-inclined Lines Problem

**Challenge**

1) You should've noticed that the corresponding angles are equal, and hence that ∆*HIG* is similar to ∆*ABC*. Can you explain why (prove that) the result is true?

2) Can you generalize further? For example: Can the equi-inclined lines lie in the extensions of sides *AB*, *BC*, and *CA*? Or does the result generalize to a quadrilateral or higher polygons? Explore!

**Note**: The above result can be viewed as a special case of Generalization 2 of a theorem by Wares given at: *Further generalizations of the theorem of Wares*. The above result is obtained by choosing *X*, *Y* and *Z* to respectively coincide with the vertices *A*, *B* and *C*.

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Created by Michael de Villiers, 24 April 2020.