Chapter 11.2, Problem 18PPS

To determine

To make: a conjecture about which triangles are congruent.

Answer to Problem 18PPS

  $\Delta ABC\cong \Delta ECD$

Explanation of Solution

Given information:

Hexagon $ABCDEF$ has six congruent sides. Segments $\overline{CA},\overline{CF},$ and $\overline{CE},$ are drawn on the hexagon, forming four triangles. Test your conjecture by measuring the sides and angles of the triangles.

  

Calculation:

Consider the figure

  

Consider four triangles $\Delta ABC,\Delta ACF,\Delta FCE$ and $\Delta ECD$ . Also consider

  $AB=AF=FE=ED=DC=CB$

In $\Delta ABC$ and $\Delta ECD$

  $\begin{array}{l}AF=FE\\ FC=FC\end{array}$

Since two sides so,

  $AC=EC$

If two triangles are congruent then their corresponding angles and their corresponding sides are congruent.

Since

  $\begin{array}{l}AB=DE\\ BC=CD\\ AC=EC\end{array}$

Therefore, $\Delta ABC\cong \Delta ECD$