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In 13,15, tell whether each conclusion follow from the given premises. If not, draw a...

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user5074879 | eNotes Newbie

Posted May 18, 2013 at 4:23 PM via web

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In 13,15, tell whether each conclusion follow from the given premises. If not, draw a counter-example.

question 13in a rhombus, diagonals are perpendicular  to each other.

                  A rhombus is a parallelogram 

                  Conclusion: in a parallelogram , diagonals  are perpendicular  to             

                  each other.

Question 15 Consecutive angles of a parallelogram  are supplementary.

                 A rhombus is a parallelogram

                Conclusion: consecutive angles of a rhombus are supplementary.

 

 

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3 Answers | Add Yours

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pramodpandey | College Teacher | Valedictorian

Posted May 18, 2013 at 4:58 PM (Answer #1)

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Q13. Rhombus is parallelogram. But in all parallelogram diagonal are nt perpendicular. For example Reactagle is parallelogram bu diagonals are not perpendicular.

Q15. Rhombus is parallelogram.Opposite sides are parallel ,so cointerior or consecutive angles are supplementry.Thus consecutive angles of rhombus are supplementry.

 

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pramodpandey | College Teacher | Valedictorian

Posted May 18, 2013 at 5:13 PM (Answer #2)

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Sorry.Please read this corrction for question 13.

In all parallelogram diagonals are perpendicular to each other.Thus in Rhombus alos diagonals are perpendicular to each other.Assertion is true.

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pramodpandey | College Teacher | Valedictorian

Posted May 19, 2013 at 3:50 AM (Answer #3)

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question 13 . In a rhombus, diagonals are perpendicular  to each other.
      A rhombus is a parallelogram

Conclusion: in a parallelogram , diagonals  are   perendicular  to each other.

Conclusion is not correct . Reactangle is parallelogram but diagonals are perpendicular.

Question 15. Consecutive angles of a parallelogram  are supplementary.

  A rhombus is a parallelogram

  Conclusion: consecutive angles of a rhombus are supplementary.

Yes ,conclusion is correct.  Co-interior angles in parallel lines , intersected by transversal are supplementry. Thus cosecutive angles of rhombus are supplementry.

 

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