Question

determine if the triangles are congruent using the definition of congruent triangles. if they are, write the congruence statement. a ( \triangle aec cong \triangle deb ) b ( \triangle abe cong \triangle dce ) c ( \triangle aeb cong \triangle dce ) d ( \triangle abc cong \triangle dcb )

Explanation:

Step1: Identify vertical angles

$\angle AEB$ and $\angle DEC$ are vertical angles. So, $\angle AEB=\angle DEC$.

Step2: Check side - angle - side (SAS) congruence

From the figure, $AE = DE$, $BE=CE$, and $\angle AEB=\angle DEC$. By the SAS (Side - Angle - Side) congruence criterion for triangles.

Step3: Write the congruence statement

For $\triangle ABE$ and $\triangle DCE$, in $\triangle ABE$ and $\triangle DCE$:

• $AE = DE$ (given)
• $\angle AEB=\angle DEC$ (vertical angles)
• $BE = CE$ (given)

So, $\triangle ABE\cong\triangle DCE$

Answer:

B. $\triangle ABE\cong\triangle DCE$