Mathematics
In the figure (2) given below, ABCD is a parallelogram, ADEF and AGHB are two squares. Prove that FG = AC.
Rectilinear Figures
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Answer
From figure,
⇒ ∠FAG + ∠GAB + ∠BAD + ∠FAD = 360° [∵ At a point total angle is 360°]
⇒ ∠FAG + 90° + 90° + ∠BAD = 360°
⇒ ∠FAG = 360 – 90° – 90° – ∠BAD
⇒ ∠FAG = 180° – ∠BAD ………(i)
⇒ ∠ABC + ∠BAD = 180° [Sum of Adjacent angle in || gm is equal to 180°]
⇒ ∠ABC = 180° – ∠BAD ………(ii)
⇒ ∠FAG = ∠ABC [From (i) and (ii)]
In || gm ABCD,
AB = CD and AD = BC.
Since, ADEF is a square,
so, AD = DE = EF = FA.
So, BC = FA.
In ∆AFG and ∆ABC, we have
⇒ AF = BC [Proved above]
⇒ AG = AB (∵ AGBH is a square)
⇒ ∠FAG = ∠ABC [Proved above]
So, ∆AFG ≅ ∆ABC by S.A.S axiom of congruency
∴ FG = AC. [By C.P.C.T]
Hence, proved that FG = AC.
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