Question

1. which statement is true by the asa postulate?

△cba ≅ △cab

△cba ≅ △abc

△cba ≅ △ade

△cba ≅ △dea

Explanation:

Step1: Recall ASA (Angle - Side - Angle) Postulate

ASA postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Step2: Analyze the given triangles

• In \(\triangle CBA\) and \(\triangle DEA\):
• \(\angle CBA=\angle DEA = 90^{\circ}\) (right angles).
• The marked equal angles: \(\angle BCA=\angle EDA\).
• The sides: \(CB = DE\) (marked as equal).

• For \(\triangle CBA\) and \(\triangle DEA\), we have two angles (\(\angle CBA,\angle BCA\)) and the included side (\(CB\)) congruent to two angles (\(\angle DEA,\angle EDA\)) and the included side (\(DE\)) of the other triangle.

Step3: Check other options

• For \(\triangle CBA\) and \(\triangle CAB\):
• \(\triangle CBA\) and \(\triangle CAB\) are not in a form to satisfy ASA.
• For \(\triangle CBA\) and \(\triangle ABC\):
• These are the same triangle (just named differently in a non - standard order, but not a congruence by ASA from two distinct triangles as required in the postulate context here).
• For \(\triangle CBA\) and \(\triangle ADE\):
• The order of angles and sides does not match the ASA postulate.

Answer:

\(\triangle CBA\cong\triangle DEA\)