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Type: Multiple-Choice
Category: Quadrilaterals
Level: Grade 10
Standards: HSG-CO.C.11
Author: nsharp1
Last Modified: 14 days ago

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Quadrilaterals Question

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Grade 10 Quadrilaterals CCSS: HSG-CO.C.11

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

Given: Quadrilateral [math]ABCD[/math] where [math]bar{AD}[/math] || [math]bar{BC}[/math] and [math]bar{AD} ~= bar{BC}[/math]
Prove: [math]bar{AB} " || " bar{CD}[/math]

Parallelogram ABCD v3

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