Chapter 12.3, Problem 27E

To determine

To prove:

The Navajo rug is made of isosceles triangles.

Explanation of Solution

Given:

The two triangle

  $\Delta ABC\cong \Delta CDE$

Concept used:

Two geometric figures are congruent if a rigid motion or a composition of rigid motions maps one of the figures onto other.

Calculation:

If two triangles are congruent.

So all the corresponding parts are congruent.

If all corresponding parts of two triangles are congruent.

So the triangle are congruent.

  $\begin{array}{l}\angle B\cong \angle D\\ \angle ABC\cong \angle CDE\\ \Delta ABC\cong \Delta CDE\end{array}$

  $\Delta ABC$ and $\Delta BCD$ and $\Delta CDE$ are isosceles triangle

Line $AB$ is congruent to line $BC$

Line $BC$ is congruent to line $CD$

Line $CD$ is congruent to line $DE$

So, by the transitive property of congruence

Angle $B$ is congruent to angle $D$

So, the triangle $ABC$ is congruent to the triangle $CDE$