Subjects geometry

Parallelogram Proof 8Bf6A3

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1. **State the problem:** Given that $AB \parallel DC$ in parallelogram $ABCD$, complete the flowchart proof to show that $\triangle ABC \cong \triangle CDA$. 2. **Given:** $AB \parallel DC$. 3. **Step 1:** $\angle BAC \cong \angle DCA$ because alternate interior angles are congruent when two lines are parallel and cut by a transversal. 4. **Step 2:** $\angle B \cong \angle D$ because opposite angles in a parallelogram are congruent. 5. **Step 3:** $AB \cong DC$ because opposite sides of a parallelogram are congruent. 6. **Step 4:** By the Angle-Side-Angle (ASA) postulate, $\triangle ABC \cong \triangle CDA$ since two angles and the included side are congruent. This completes the proof.