Question

geo h hw on proving as b duelin by sss or sas. justinc
given: b mopt ad
prove: a eba ≅ △cbo

Explanation:

Step1: State the given information

$B$ is the midpoint of $\overline{AO}$. So, $\overline{AB}\cong\overline{OB}$.

Step2: Identify vertical angles

$\angle EBA$ and $\angle CBO$ are vertical angles. By the Vertical Angles Theorem, $\angle EBA\cong\angle CBO$.

Step3: Use the given side - side congruence

Given that $\overline{EA}\cong\overline{CO}$.

Step4: Apply the SAS (Side - Angle - Side) congruence criterion

In $\triangle EBA$ and $\triangle CBO$, we have $\overline{EA}\cong\overline{CO}$, $\angle EBA\cong\angle CBO$, and $\overline{AB}\cong\overline{OB}$. So, by the SAS congruence criterion, $\triangle EBA\cong\triangle CBO$.

Answer:

Statements	Reasons
$\overline{AB}\cong\overline{OB}$	Definition of midpoint
$\angle EBA\cong\angle CBO$	Vertical Angles Theorem
$\overline{EA}\cong\overline{CO}$	Given
$\triangle EBA\cong\triangle CBO$	SAS ($\overline{EA}\cong\overline{CO}$, $\angle EBA\cong\angle CBO$, $\overline{AB}\cong\overline{OB}$)