Question

8. In the figure, ADC is a straight line.
(a) Prove that triangle ABC ~ triangle BDC.
(b) Find the length of BD.
​

Answer 1

Answer:

a). ΔABC ~ ΔBDC

b). m(BD) = 6 units

Step-by-step explanation:

If ΔABC ~ ΔBDC,

a). Ratio of the corresponding sides of both the triangles will be equal.

$\frac{AB}{BD}=\frac{BC}{DC}=\frac{AC}{BC}$

$\frac{BC}{DC}=\frac{AC}{BC}$

$\frac{12}{9}=\frac{7+9}{12}$

$\frac{4}{3}=\frac{4}{3}$

Since Ratio of the corresponding sides are same, therefore, both the triangles are similar.

b). $\frac{AB}{BD}=\frac{BC}{DC}$

$\frac{8}{BD}=\frac{12}{9}$

BD = $\frac{9\times 8}{12}$

BD = 6