Question

Decide whether triangles ABC and DEC are similar. Explain or show your reasoning.

Answer 1

Given the triangles ABC and DEC

For the triangle ABC:

m∠A = 36, m∠B = 21

So, the m∠C = 180 - (m∠A + m∠B ) = 180 - (36 + 21) = 123

So, comparing the measurements of the angles of both triangles:

$\begin{gathered} m\angle A=m\angle D=36\degree \\ m\angle\text{ACB}=m\angle\text{DCE}=123\degree \end{gathered}$

So, the triangles are similar using the AA postulate.

So,

$\triangle\text{ABC}\sim\triangle\text{DEC}$