Question

1. which is not a pair of congruent angles in the diagram below?

diagram of triangles aeb and cdb intersecting at b, with angle markings
options:

• $\angle eab \cong \angle cdb$
• $\angle aeb \cong \angle cdb$
• $\angle abe \cong \angle dbc$
• $\angle aeb \cong \angle dcb$

Explanation:

Step1: Analyze Vertical Angles

Vertical angles are congruent. $\angle ABE$ and $\angle DBC$ are vertical angles, so $\angle ABE \cong \angle DBC$.

Step2: Analyze Marked Angles

From the diagram, $\angle EAB$ and $\angle CDB$ have the same marking (single arc), $\angle AEB$ and $\angle DCB$ have the same marking (double arc), $\angle AEB$ and $\angle CDB$ have different markings (double vs single arc). So $\angle AEB
ot\cong \angle CDB$.

Step3: Verify Other Pairs

$\angle EAB$ (single arc) and $\angle CDB$ (single arc) are congruent. $\angle AEB$ (double arc) and $\angle DCB$ (double arc) are congruent.

Answer:

$\angle AEB \cong \angle CDB$ (the option stating $\angle AEB \cong \angle CDB$ is not a pair of congruent angles)