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]
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]
| [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] |
- Reflexive Property
- Diagonals of a parallelogram are congruent
- Given by the diagram
- Corresponding sides of congruent triangles are congruent
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