7. In the adjoining figure, ABCD is a rectangle. Prove
that AC = BD.
[Hint. AABC ABAD]
6
B
Answers
Answer:
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Given : ABCD is a rectangle.
To Find : Prove that AC=BD
Solution:
in ΔABC and ΔBAD
AB = BA Common
∠ABC = ∠BAD = 90°
BC = AD ( opposite sides of rectangle )
=> ΔABC ≅ ΔBAD ( SAS congruence)
Corresponding parts of congruent triangle are congruent
Hence
AC ≅ BD
=> AC = BD
QED
Hence Proved
Another method :
Using Pythagorean theorem
square on the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two perpendicular sides.
AC² = AB² + BC²
BD² = AB² + AD²
BC = AD opposite sides of rectangle
=> AC² = BD²
=> AC = BD
QED
Hence Proved
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