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AB and CD are respectively the smallest and the longest sides of quadrilateral ABCD. Show that angel A > angel C?
Verified Answer
AB and CD are respectively the smallest and the longest sides of quadr...
In ΔABC, we have
BC > AB
⇒ ∠BAC > ∠BCA ...(1)
Similarly, in ΔACD, we have
CD > AD
⇒ ∠CAD > ∠ACD ...(2)
On adding (1) and (2), we get
∠BAC + ∠CAD > ∠BCA + ∠ACD
⇒∠BAD > ∠BCD
⇒ ∠A > ∠C
Hence, it is proved that ∠A > ∠C
This question is part of UPSC exam. View all Class 9 courses
Most Upvoted Answer
AB and CD are respectively the smallest and the longest sides of quadr...
Given:
In quadrilateral ABCD, AB smallest & CD is longest sides.
To Prove: ∠A>∠C
& ∠B>∠D
Construction: Join AC.
Mark the angles as shown in the figure..
Proof:
In △ABC , AB is the shortest side.
BC > AB
∠2>∠4 …(i)
[Angle opposite to longer side is greater]
In △ADC , CD is the longest side
CD > AD
∠1>∠3 …(ii)
[Angle opposite to longer side is greater]
Adding (i) and (ii), we have
∠2+∠1>∠4+∠3
⇒∠A>∠C
Similarly, by joining BD, we can prove that
∠B>∠D
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AB and CD are respectively the smallest and the longest sides of quadrilateral ABCD. Show that angel A > angel C?
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AB and CD are respectively the smallest and the longest sides of quadrilateral ABCD. Show that angel A > angel C? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about AB and CD are respectively the smallest and the longest sides of quadrilateral ABCD. Show that angel A > angel C? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for AB and CD are respectively the smallest and the longest sides of quadrilateral ABCD. Show that angel A > angel C?.
AB and CD are respectively the smallest and the longest sides of quadrilateral ABCD. Show that angel A > angel C? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about AB and CD are respectively the smallest and the longest sides of quadrilateral ABCD. Show that angel A > angel C? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for AB and CD are respectively the smallest and the longest sides of quadrilateral ABCD. Show that angel A > angel C?.
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