Question

given the two congruent triangles, list all the corresponding angles and sides.
\\( \angle dca \cong \\)
\\( \angle dac \cong \\)
\\( \angle d \cong \\)
\\( ab \cong \\)
\\( ac \cong \\)
\\( ad \cong \\)

Explanation:

Step1: Identify congruent triangles

Since \( \triangle ABC\cong\triangle CDA\) (by SSS or SAS congruence criteria, as \(AB = CD\), \(BC=DA\), \(AC = CA\) (common side) or \(AB = CD\), \(\angle BAC=\angle DCA\), \(AC = CA\)).

Step2: Find corresponding angles

• For angles:
• \(\angle B\) corresponds to \(\angle D\) (as per congruent triangle properties).
• \(\angle BCA\) corresponds to \(\angle DAC\) (by congruence).
• \(\angle BAC\) corresponds to \(\angle DCA\) (by congruence).
• For sides:
• \(AB\cong CD\) (given or by congruence).
• \(BC\cong DA\) (given or by congruence).
• \(AC\cong CA\) (common side, reflexive property).

Answer:

\(\angle B\cong\angle D\), \(\angle BCA\cong\angle DAC\), \(\angle BAC\cong\angle DCA\), \(AB\cong CD\), \(BC\cong DA\), \(AC\cong CA\)