Question

Question 6 In the following figure, if ΔABE ≅ ΔACD, show that ΔADE ∼ ΔABC.

Class 10 - Math - Triangles Page 140

Answer 1

°.° ∆ABE ~= ∆ACD

.°. AB = AC ( CPCT )

and

AE = AD ( CPCT )

.°. AB/AC = 1 --------------(1)

and

AD/AE = 1 ----------(2)

from (1) and (2) ,

AB/AC = AD/AE

.°. ∆ADE and ∆ABCs

AD/AE = AB/AC

<A = <A

.°. ∆ ADE ~ ∆ABC ( Criteria of SAS )

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Answer 2

It is given that ΔABE ≅ ΔACD.
∴ AB = AC [By cpct] ...(i)
And, AD = AE [By cpct] ...(ii)
In ΔADE and ΔABC,

AD/AB = AE/AC [Dividing equation (ii) by (i)]

∠A = ∠A [Common angle]
∴ ΔADE ~ ΔABC [By SAS similarity criterion]