Question

In triangles ABC and PQR, AB = 3.5 cm, BC = 7.1 cm, AC = 5 cm, PQ = 7.1 cm,

QR = 5 cm and PR = 3.5 cm. Examine whether the two triangles are congruent or

not. If yes, write the congruence relation in symbolic form.​

Answer 1

BY S S S{SIDE SIDE SIDE} CRITERIA, THE TRIANGLES ARE CONGRUENT.

THE CORRECT CORRESPONDENCE IS :-

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TRIANGLE ABC = TRIANGLE RPQ

AB = RP

BC = PQ

AC = RQ

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Answer 2

Here,

AB= PR (=3.5cm),

BC= PQ (=7.1cm)

AC = QR (= 5cm)

:-This shows that three sides of one triangle are equal to the three sides of the other triangle . So,by the SSS congruence rule,the two triangles are congruent. From the above three equality relations , it can be easily seen that A ⟷ R,B⟷P and C ⟷ Q.

So,we have

∆ABC = ∆RPQ.

$\sf\underline\bold{Important-note}$

The order of the letters in the names of congruent triangles displays the corresponding relationships . Thus,when you write ∆ABC =∆RPQ,you would know that A lies on R,B on P,C on Q , AB along RP , BC along PQ and AC along RQ.

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