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Abcd is a Kite in Which Bc = Cd, Ab = Ad. E, F and G Are the Mid-points of Cd, Bc and Ab Respectively. Prove That: ∠Efg = 90° - Mathematics

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Question

ABCD is a kite in which BC = CD, AB = AD. E, F and G are the mid-points of CD, BC and AB respectively. Prove that: ∠EFG = 90°

Sum
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Solution


Diagonals of a kite intersect at right angles
∴ ∠MON = 90°     .......(i)
In ΔBCD,
E and F are mid-points of CD and BC respectively.

Therefore, EF || DB and EF = `(1)/(2)"DB"`       .......(ii)

EF || DB ⇒ MF || ON
∴ ∠MON + ∠MFN = 180°
⇒ 90° + ∠MFN = 180°
⇒  ∠MFN = 90°
⇒  ∠EFG = 90°.

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Chapter 15: Mid-point and Intercept Theorems - Exercise 15.1

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Frank Mathematics [English] Class 9 ICSE
Chapter 15 Mid-point and Intercept Theorems
Exercise 15.1 | Q 22.1

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