Q) In the give figure, AB ǁ DE and AC ǁ DF. Show that Δ ABC ~ Δ DEF. If BC = 10cm, EB = CF = 5 cm and AB =7 cm, then find the length DE.

(Q 21 – 30/5/2 – CBSE 2026 Question Paper)

Ans:

(i) Prove that Δ ABC ~ Δ DEF

Step 1: Here, ∵ AB ǁ DE, and line EF cuts these lines

∴ ∠ DEF = ∠ ABC             

(being corresponding angles)

Step 2: AC ǁ DF, and line EF cuts these

∴ ∠ DFE = ∠ ACB           

(being corresponding angles)

Step 3: Next, Let’s compare Δ ABC with Δ DEF 

∠ DEF = ∠ ABC               (from step 1)

∠ DFE = ∠ ACB               (from step 2)

∴ by AA similarity criterion:

Δ ABC ~ Δ DEF…. Hence Proved !

(ii) Length of DE:

Since, Δ ABC ~ Δ DEF (proved above)

∴ …… (i)

Given that AB = 7 cm, BC = 10 cm,

and EB = CF = 5 cm

Now, from the diagram, EF = EB + BC + CF

∴  EF = 5 + 10 + 5 = 20 cm

Now by substituting the values in equation (i), we get:

∴ …… (i)

∴ = 2

∴ DE = 2 x 7 = 14 cm

Therefore, length of DE is 14 cm.

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