What can you say about the gray triangle that's wedged in between △ ABC and △ CDE?
See solution.
Practice makes perfect
Let's isolate the pieces we need from the rug. Note that we need the gray triangle, △ BCD, that's wedged in between △ ABC and △ CDE, as well. Let's also add the given information ∠ B ≅ ∠ D to the diagram.
Notice that the exercise claims that the Navajo rug is made of isosceles triangles. That would include the gray triangle △ BCD. Therefore, we know that BC≅ DC. Let's add this to the diagram.
Again, all triangles are isosceles, including the yellow ones, which would imply that
BA ≅ BC and DC ≅ DE
Since BC≅ DC, by the Transitive Property of Congruence, each of the these four sides are congruent to each other. Let's also add this information to the diagram.
Since two sides and the included angle of one triangle are congruent to two sides and the included angle of the second triangle, we can by the SAS Congruence Theorem prove that the triangles are congruent.
△ ABC ≅ △ CDE
