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Home » In ΔABC, ∠ABC = ∠DAC, AB = 8 cm, AC = 4 cm and AD = 5 cm. (i) Prove that ΔACD is similar to ΔBCA. (ii) Find BC and CD
In ΔABC, ∠ABC = ∠DAC, AB = 8 cm, AC = 4 cm and AD = 5 cm. (i) Prove that ΔACD is similar to ΔBCA. (ii) Find BC and CD
Class 10 | Exercise 15E | ICSE | Maths | Selina | Similarity (With Applications to Maps and Models)
In ΔABC, ∠ABC = ∠DAC, AB = 8 cm, AC = 4 cm and AD = 5 cm. (i) Prove that ΔACD is similar to ΔBCA. (ii) Find BC and CD

Selina Solutions Concise Class 10 Maths Chapter 15 ex. 15(E) - 12

Solution:

(i) In

    \[\vartriangle ACD\text{ }and\text{ }\vartriangle BCA\]

    \[\angle DAC\text{ }=\angle ABC\]

[Given]

    \[\angle ACD\text{ }=\angle BCA\]

[Common angles]

Hence,

    \[\vartriangle ACD\text{ }\sim\text{ }\vartriangle BCA\text{ }by\text{ }AA\]

criterion for similarity.

 

(ii) Since,

    \[\vartriangle ACD\text{ }\sim\text{ }\vartriangle BCA\]

We have,

    \[AC/BC\text{ }=\text{ }CD/CA\]

    \[=\text{ }AD/AB\]

So,

    \[4/BC\text{ }=\text{ }CD/4\text{ }=\text{ }5/8\]

    \[4/BC\text{ }=\text{ }5/8\]

So,

    \[BC\text{ }=\text{ }32/5\text{ }=\text{ }6.4\text{ }cm\]

And,

    \[CD/4\text{ }=\text{ }5/8\]

Thus,

    \[CD\text{ }=\text{ }20/8\text{ }=\text{ }2.5\text{ }cm\]

i

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