Question

In triangle ABC, D and E are the points on sides AB and AC respectively. If AB = 18 cm, AD = 8 cm, AE = 12 cm and EC = 15 cm, then which of the following conditions is/are true?

• A. $DE\parallel BC$
• B. AE = AD
• C. $\angle ADE=\angle ACB$
• D. DE = BD

Answer 1

The correct option is A

$DE\parallel BC$

$\text{Given :}AB=18cm,AD=8cm,AE=12cm\text{and}EC=15cm$

$\therefore DB=AB-AD=18-8=10\text{cm}$

$\text{Now,}\frac{AD}{DB}=\frac{8}{10}=\frac{4}{5}$

$\text{and}\frac{AE}{EC}=\frac{12}{15}=\frac{4}{5}$

$\because \frac{AD}{DB}=\frac{AE}{EC}$

$\therefore DE\parallel BC\text{(By converse of basic proportionality}\text{theorem)}$