Questions: Step 1: ABCD is a parallelogram Step 2: ∠CDA ≅ ∠BAD, ∠CAD ≅ ∠BDA Step 3: Reflexive Property Step 4: △CIDA ≅ △BAD

△ Prove that \( \triangle CDA \sim \triangle BAD \) using the properties of a parallelogram. ○ Analyze given information. ▷ Identify that ABCD is a parallelogram and note its properties. ☼ ABCD is a parallelogram, so opposite sides are parallel and congruent. This is the given information. ○ Identify congruent angles. ▷ Use the properties of parallelograms and alternate interior angles to find congruent angles. ☼ Since ABCD is a parallelogram, alternate interior angles are congruent. Thus, \( \angle CDA \cong \angle BAD \) and \( \angle CAD \cong \angle BDA \). This follows from the Alternate Interior Angles Theorem. ○ Apply the reflexive property. ▷ Identify the common side between the two triangles. ☼ The segment \( AD \) is common to both \( \triangle CDA \) and \( \triangle BAD \). Therefore, \( AD \cong AD \) by the Reflexive Property. ○ Establish triangle similarity. ▷ Use angle congruence and the reflexive property to prove similarity. ☼ We have \( \angle CDA \cong \angle BAD \) (from the properties of a parallelogram) and \( AD \cong AD \) (reflexive property). Additionally, \( \angle CAD \cong \angle BDA \) (alternate interior angles). Using the ASA Similarity Postulate, \( \triangle CDA \sim \triangle BAD \). Alternatively, using \( \angle ACD \cong \angle BAC \), we can apply the AAS Similarity Postulate to reach the same conclusion. ✧ The triangles \( \triangle CDA \) and \( \triangle BAD \) are similar by either the ASA or AAS Similarity Postulate. ☺

Step 2: Alternate Interior Angles Theorem Step 3: AD ≅ AD Step 4: ΔCDA ~ ΔBAD, ASA Similarity Postulate (or AAS Similarity Postulate).