Question

cw/hw on proving △s ≅ by asa or aas
①
prove: △eao ≅ △abc

Explanation:

Step1: Identify Parallel Lines and Alternate Interior Angles

Since \( EO\parallel AB\) and \( AO\) is a transversal, \(\angle EOA=\angle BAC\) (alternate - interior angles). Also, since \( AB\parallel DC\) and \( AC\) is a transversal, \(\angle OAE=\angle DCA\) (alternate - interior angles).

Step2: Use the ASA (Angle - Side - Angle) Criterion

We know that \( AO = AC\) (given). In \(\triangle EAO\) and \(\triangle ABC\):

• \(\angle EOA=\angle BAC\) (from step 1)
• \(AO = AC\) (given)
• \(\angle OAE=\angle DCA\) (from step 1)

By the ASA (Angle - Side - Angle) congruence criterion, \(\triangle EAO\cong\triangle ABC\)

Answer:

\(\triangle EAO\cong\triangle ABC\) by the ASA congruence criterion.