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Question
Using the information given of the following figure, find the values of a and b.
Solution
In ΔAEB and ΔCAD,
∠EAD = ∠CAD .........[Given]
∠ADC = ∠AEB .......[∵ ∠ADE = ∠AED { AE = AD }180° − ∠ADE = 180° − ∠AED = ∠ADC = ∠AEB]
AE = AD .........[Given]
∴ ΔAEB ≅ ΔCAD ....[ASA]
AC = AB .......[By C.P.C.T.]
2a + 2 = 7b − 1
⇒ 2a − 7b = − 3 ....(i)
CD = EB
⇒ a = 3b ....(ii)
Solving (i) and (ii), We get,
a = 9, b = 3
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