Question

(i) Determine if the triangles below are similar, and explain how you know.

(ii) Find the lengths of the missing sides. All measures are centimeters unless otherwise
stated.

Answer 1

d = 12 cm

Explanation:

Let small triangle and large triangles be given by
`\triangle _1\:\&\: \triangle _2\\`

Let the Marked angels of
`\triangle _1` be

`\angle 1\: \&\: \angle 2\\`

Similarly Marked angels of
`\triangle _2` be
`\angle 3\: \&\: \angle 4\\`

`\therefore \angle 1\cong \angle 3...(given) \\</p><p>\& \angle 2\cong \angle 4...(given) \\</p><p>\therefore \triangle _1\sim \triangle _2.. (By\: AA\:Postulate) \\</p><p>\therefore (5)/(15)=(4)/(d)..(By\: csst) \\</p><p>\therefore d =(15* 4)/(5) \\</p><p>\therefore d =3* 4\\</p><p>\huge \purple {\boxed {\therefore d =12\: cm}} \\`