Answer:
a) DE is 12 cm
b) CE is 2 cm
Step-by-step explanation:
In the two triangles [tex]\triangle ABC[/tex] and [tex]\triangle ADE[/tex].
[tex]\angle A[/tex] is common.
BC || DE
[tex]\Rightarrow \angle B = \angle D\ and \\ \Rightarrow \angle C = \angle E[/tex]
[tex]\because[/tex] 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:
[tex]\triangle ABC[/tex] [tex]\sim[/tex] [tex]\triangle ADE[/tex].
Ratio of corresponding sides of two similar triangles are always equal.
[tex]\dfrac{AB}{AD} = \dfrac{BC}{DE}\\\Rightarrow \dfrac{9}{9+3} = \dfrac{9}{DE}\\\Rightarrow \dfrac{9}{12} = \dfrac{9}{DE}\\\Rightarrow DE = 12\ cm[/tex]
[tex]\dfrac{AB}{AD} = \dfrac{AC}{AE}\\\Rightarrow \dfrac{9}{9+3} = \dfrac{6}{AC+CE}\\\Rightarrow \dfrac{9}{12} = \dfrac{6}{6+CE}\\\Rightarrow 6+CE = \dfrac{4\times 6}{3}\\\Rightarrow 6+CE = 8\\\Rightarrow CE = 2\ cm[/tex]
So, the answers are:
a) DE is 12 cm
b) CE is 2 cm
