Question

The triangle ADE
BC is parallel to DE
AB = 9cm, AC = 6cm, BD = 3cm, BC = 9cm

Answer 1

a) DE is 12 cm

b) CE is 2 cm

Explanation:

In the two triangles
`\triangle ABC` and
`\triangle ADE`.

`\angle A` is common.

BC || DE

`\Rightarrow \angle B = \angle D\ and \\ \Rightarrow \angle C = \angle E`

`\because` two parallel lines BC and DE are cut by BD and CE respectively and the angles are corresponding angles.

All three angles are equal hence, the triangles:

`\triangle ABC`
`\sim`
`\triangle ADE`.

Ratio of corresponding sides of two similar triangles are always equal.

`(AB)/(AD) = (BC)/(DE)\\\Rightarrow (9)/(9+3) = (9)/(DE)\\\Rightarrow (9)/(12) = (9)/(DE)\\\Rightarrow DE = 12\ cm`

`(AB)/(AD) = (AC)/(AE)\\\Rightarrow (9)/(9+3) = (6)/(AC+CE)\\\Rightarrow (9)/(12) = (6)/(6+CE)\\\Rightarrow 6+CE = (4* 6)/(3)\\\Rightarrow 6+CE = 8\\\Rightarrow CE = 2\ cm`

So, the answers are:

a) DE is 12 cm

b) CE is 2 cm