Question

In the given figure, $A B ∥ D E$ and $A C ∥ D F$ . Show that $△ A BC \sim △ D EF$ . If $BC = 10$ cm, $EB = CF = 5$ cm and $A B = 7$ cm, then find the length DE.

Approach

Since AB is parallel to DE and AC is parallel to DF, corresponding angles are equal: $∠ D EF = ∠ A BC$ and $∠ D FE = ∠ A CB$ . By AA similarity, $△ A BC \sim △ D EF$ . Using the similarity ratio, $\frac{BC}{EF} = \frac{A B}{D E}$ , we get $\frac{10}{20} = \frac{7}{D E}$ , thus $D E = 14$ cm.

Step-by-step working

1
Since $A B ∥ D E$ , $∠ D EF = ∠ A BC$ . Since $A C ∥ D F$ , $∠ D FE = ∠ A CB$ . Hence $△ A BC \sim △ D EF$ by AA criterion.
1 mark
2
From similarity, $\frac{BC}{EF} = \frac{A B}{D E} \Rightarrow \frac{10}{20} = \frac{7}{D E} \Rightarrow D E = 14$ cm.
1 mark

Concepts used

similar trianglesparallel linesshow thatfind length

Approach

Step-by-step working

Concepts used

Similar question types