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Type: Multiple-Choice
Standards: HSG-CO.C.11
Author: nsharp1

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What is the missing reason in step 4 of the following proof?

Given: Quadrilateral $ABCD$ where $bar{AD}$ || $bar{BC}$ and $bar{AD} ~= bar{BC}$
Prove: $bar{AB} " || " bar{CD}$

 $\ \ \ \ \ \ \ \ \ \ \ \ " Statement " \ \ \ \ \ \ \ \ \ \ \ \$ $" Reason "$ $1. bar{AD} " || " bar{BC}$ $1. "Given"$ $2. ang CBD ~= ang ADB$ $2. "Alternate interior angles are congruent"$ $3. bar{BC} ~= bar{AD}$ $3. "Given"$ $4. bar{BD} ~= bar{BD}$ $4. ""$ $5. Delta ABD ~= Delta CDB$ $5. "Side-Angle-Side Postulate"$ $6. ang ABD ~= ang CDB$ $6. "Corresponding angles of congruent triangles are congruent"$ $7. bar{AB} " || " bar{CD}$ $7. "If two lines are cut by a transversal, and alternate interior"$ $\ \ \ \ \ " angles are congruent, the lines are parallel"$
1. Reflexive Property
2. Diagonals of a parallelogram are congruent
3. Given by the diagram
4. Corresponding sides of congruent triangles are congruent
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