Question

In the triangle ABC, AB = 5 cm,  A = x0 ,  B = y0 , BC = 4 cm, AC = 3.5 cm
• In the triangle PQR,  P = x0
, PQ = 10 cm, PR = 7 cm
• In the triangle DEF,  D = x0 ,  E= y0
. EF = 7 cm
1. Examine whether these triangles are similar
(Hint : What are the different contexts of similarly of trinagles?)

Answer 1

Given :-

• In the triangle ABC, AB = 5 cm, ∠A = x° , ∠B = y° , BC = 4 cm, AC = 3.5 cm .

• In the triangle PQR, ∠P = x° , PQ = 10 cm, PR = 7 cm .

• In the triangle DEF, ∠D = x° , ∠E= y° , EF = 7 cm .

To Find :- Examine whether these triangles are similar .

In ∆ABC and ∆PQR ,

→ ∠BAC = ∠QPR { given x°}

→ AB/PQ = AC/PR = 5/10 = 3.5/7 = 1/2 = 1/2 .

therefore,

→ ∆ABC ~ ∆PQR { By SAS similarity. } -------- Eqn.(1)

In ∆ABC and ∆DEF,

→ ∠BAC = ∠EDF { given x°}

→ ∠ABC = ∠DEF { given y°}

therefore,

→ ∆ABC ~ ∆DEF { By AA similarity. } --------- Eqn.(2)

hence, from Eqn.(1) and Eqn.(2)

→ ∆PQR ~ ∆DEF .

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Answer 2

Answer:

In the triangle ABC, AB = 5 cm,  A = x0 ,  B = y0 , BC = 4 cm, AC = 3.5 cm

• In the triangle PQR,  P = x0

, PQ = 10 cm, PR = 7 cm

• In the triangle DEF,  D = x0 ,  E= y0

. EF = 7 cm

1. Examine whether these triangles are similar

(Hint : What are the different contexts of similarly of trinagles?)