Question

In the given triangle PQR, AB || QR, QP || CB and AR intersects CB at O. P B 3c 6c С 4c R Q Using the given diagram answer the following question: The triangle similar to AARQ is (b) AARP (C) AOBR (a) AORC (d) AQRP (1) APQR ~ABCR by axiom (b)AAA (a) SAS (c) SSS (d) AAS If QC =6 cm, CR = 4 cm, BR = 3 cm. The length of RP is (b) 8cm (c) 7.5cm (a) 4.5 cm (d) 5cm (iv) The ratio PQ: BC is (a) 2:3 (b) 3:2 (c) 5:2 (d) 2:5​

Answer 1

∆ARQ~∆ORC

∆PQR~∆BCR by AAA axiom

7.5 cm

5:2

Answer 2

(1) In ∆ARQ and ∆ORC we have ,

→ QA || CO { given that, QP || CB . }

therefore,

→ ∠QAR = ∠COR { Corresponding angles. }

→ ∠ARQ = ∠ORC { Common angles. }

therefore,

→ ∆ARQ ~ ∆ORC { By AA similarity. }

therefore, (a) ∆ORC is correct answer .

 

(2)

since,

→ QP || CB,

In ∆PQR and ∆BCR we have,

→ ∠PQR = ∠BCR { Corresponding angles. }

→ ∠PRQ = ∠BRC { Common angles. }

→ ∠QPR = ∠CBR { Corresponding angles. }

So,

→ ∆PQR ~ ∆BCR { By AAA similarity. }

therefore, (b) AAA is correct answer .

(3)

since,

→ ∆PQR ~ ∆BCR

→ QR/CR = RP/RB

→ (6+4)/4 = RP/3

→ 10/4 = RP/3

→ RP = 30/4

→ RP = 7.5 cm (C)

(4)

similarly,

→ PQ/BC = QR/CR

→ PQ/BC = 10/4

→ PQ/BC = 5/2

→ PQ : BC = 5 : 2 (c)