Question

8. If in two As ABC and DEF, , then

(a) ∆ABC ~ ∆DEF

(b) ∆ABC ~ ∆EDF

(c) ∆ABC ~ ∆EFD

(d) ∆ABC ~ ∆DFE

9. It is given that ∆ABC ~ ∆DEF and . Then is equal to

(а) 5

(b) 25

(c)

(d)

10. In ∠BAC = 90° and AD ⊥ BC. A Then

(а) BD.CD = BC²

(б) AB.AC = BC²

(c) BD.CD = AD²

(d) AB.AC = AD²

11. D and E are respectively the points on the sides AB and AC of a triangle ABC such that AD

= 2 cm, BD = 3 cm, BC = 7.5 cm and DE || BC. Then, length of DE (in cm) is

(a) 2.5

(b) 3

(c) 5

(d) 6

​

Answer 1

Given : ∠BAC = 90° and AD ⊥ BC

To Find :  Correct option :

(а) BD.CD = BC²

(b) AB.AC = BC²

(c) BD.CD = AD²

(d) AB.AC = AD²

Solution:

ΔADB and ΔCDA

∠ADB = ∠CDA  = 90°

∠DBA =   ∠DAC   = 90° - ∠C

=> ΔADB ≈ ΔCDA ( AA)

=> AD/CD = BD/ AD

=> AD² = BD. CD

BD.CD = AD²

is the correct option

ΔADE ≈ ΔABC

=> AD/AB  = DE/BC

=> AD/(AD + BD)  = DE/BC

=> 2/(2 + 3) = DE/7.5

=> 2/5 = DE/7.5

=> DE = 3

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Answer 2

Answer:

If in two As ABC and DEF, ABDF=BCFE=CAED, then

(a) ∆ABC ~ ∆DEF

(b) ∆ABC ~ ∆EDF

(c) ∆ABC ~ ∆EFD

(d) ∆ABC ~ ∆DFE