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anonymous

  • one year ago

I need help with this proof: In parallelogram ABCD, AE and CF are perpendicular to diagonal BD, and EF = 10 cm. If BD = 28 cm, then how long are DE and BF? Given: ABCD is Parallelogram, AE and CF are perpendicular to diagonal BD, EF = 10 cm. BD = 28 Prove: How long are DE and BF Statements Reasons 1 ABCD is a parallelogram 1 Given 2 AE and CF are perpendicular to diagonal BD. 2 Given 3 AD is parallel to BC 3 4 Angle ADE is congruent to angle CBF 4 5 Angle AED and angle CFB are right angles. 5 6 Angle AED is congruent to angle CFB 6 7 AD is congruent to BC 7 8 Triangle AED is congruent to triangle CFB 8 9 DE is congruent to BF 9 10 EF = 10 and BD = 28 10 11 BD = DE + EF + FB 11 12 28 = DE + 10 + FB 12 13 18 = DE + FB 13 14 DE = FB 14 15 18 = 2(DE) 15 16 9 = DE = FB 16

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  1. Loser66
    • one year ago
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    9

  2. Loser66
    • one year ago
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    You get nothing if you don't make any question on it.

  3. mathstudent55
    • one year ago
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    Are all the statements given in the problem and you need to supply the missing reasons?

  4. anonymous
    • one year ago
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    I am having trouble coming up with the reasons

  5. mathstudent55
    • one year ago
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    Are the statements given in the problem?

  6. mathstudent55
    • one year ago
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    Also, do you have a figure?

  7. anonymous
    • one year ago
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    Yes - all the statements are provided and I just need to provide the reasons. Please see the figure attached. Thanks.

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  8. mathstudent55
    • one year ago
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    |dw:1436807340394:dw|

  9. mathstudent55
    • one year ago
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    |dw:1436807651551:dw|

  10. Loser66
    • one year ago
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    Statements Reasons 1. ABCD is a parallelogram : Given 2. AE and CF are perpendicular to diagonal BD: Given 3. AD is parallel to BC: Property of parallelogram 4. Angle ADE is congruent to angle CBF : Alternate interior angles. 5. Angle AED and angle CFB are right angles: given 6. Angle AED is congruent to angle CFB: both are 90 degree from 5 7. AD is congruent to BC: Sides of parallelogram 8. Triangle AED is congruent to triangle CFB: conclusion from4,5,6,7 9. DE is congruent to BF : Result from8 10. EF = 10 and BD = 28: Given 11. BD = DE + EF + FB: From10 12. 28 = DE + 10 + FB: Replace the given information 13. 18 = DE + FB: Minus 10 both sides 14. DE = FB: From 9 15. 18 = 2(DE) 16. 9 = DE = FB : Divide both sides by 2and from14.

  11. mathstudent55
    • one year ago
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    1. Given 2. Given 3. Definition of parallelogram. 4. Theorem of alternate interior angles of parallel lines 5. Definition of perpendicular lines 6. Theorem: All right angles are congruent 7. Theorem: opposite sides of a parallelogram are congruent 8. AAS 9. CPCTC 10. Given 11. Segment addition postulate 12. Substitution property of equality 13. Subtraction property if equality 14. Definition of congruent segments 15. Substitution 16. Division prop of equality & transitive prop of equality

  12. anonymous
    • one year ago
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    Can someone help me with the attached proof? The statements are given, I am having problems with the Reasons 5, 6 and 7. Thanks

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  13. mathstudent55
    • one year ago
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    Reason 2: A property of proportions. In my opinion, there are two statements missing here. Statement 2a. XR + RQ = XQ Reason 2a. Segment addition postulate Statement 2b. YS + SQ = SQ Reason 2b. Segment addition postulate Reason 3. Substitution property of equality Reason 4. If two triangles have 2 pairs of corresponding sides with proportional lengths and a pair of corresponding congruent included angles, then the triangles are similar. Reason 6. Definition of similar triangles. Reason 7. If two lines are cut by a transversal, such that corresponding angles are congruent, then the lines are parallel.

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