Question

In ΔABC, ∠A=30°, ∠B=40° and ∠C=110°
In ΔPQR, ∠P=30°, ∠Q=40° and ∠R=110°
A student says that DABC @ DPQR by AAA congruence criterion. Is he justified? Why or why not?

Answer 1

Hi ,

It is given that ,

In ∆ABC , <A = 30° , <B = 40° , <C = 110° ;

In ∆PQR , <P = 30° , <Q = 40° , <R = 110° :

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In two triangles , if the angles are equal,

then the sides opposite to the equal

equal angles are in the same ratio

( or proportional ) and hence the two

triangles are similar .

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Here ,

<A = <P ,

<B = <Q ,

<C = <R

Therefore ,

∆ABC ~ ∆PQR

All congruent figure's are similar but all

similar figures are not congruent.

I hope this helps you.

: )