Question

8. In the figure, ADC is a straight line.

(a) Prove that triangle ABC ~ triangle BDC.
(b) Find the length of BD.
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Answer 1

a). ΔABC ~ ΔBDC

b). m(BD) = 6 units

Explanation:

If ΔABC ~ ΔBDC,

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

`(AB)/(BD)=(BC)/(DC)=(AC)/(BC)`

`(BC)/(DC)=(AC)/(BC)`

`(12)/(9)=(7+9)/(12)`

`(4)/(3)=(4)/(3)`

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

b).
`(AB)/(BD)=(BC)/(DC)`

`(8)/(BD)=(12)/(9)`

BD =
`(9* 8)/(12)`

BD = 6