determine if the triangles are similar. if so, state the postulate or theorem and write the similarity…
determine if the triangles are similar. if so, state the postulate or theorem and write the similarity statement.
Answer
Explanation:
Step1: Identify vertical angles
$\angle AEB$ and $\angle DEC$ are vertical - angles, so $\angle AEB=\angle DEC$.
Step2: Check for congruent sides
We are given that $\overline{AE}\cong\overline{DE}$ and $\overline{BE}\cong\overline{CE}$.
Step3: Apply the Side - Angle - Side (SAS) similarity theorem
Since $\frac{AE}{DE} = 1$, $\frac{BE}{CE}=1$ and $\angle AEB=\angle DEC$, by the SAS similarity theorem, $\triangle AEB\sim\triangle DEC$.
Answer:
The triangles $\triangle AEB$ and $\triangle DEC$ are similar by the Side - Angle - Side (SAS) similarity theorem.