In -ABC- -A-30- -B-40- and -C-110-In -PQR- -P-30- -Q-40- and -R-110-A student says that -ABC-PQR by AAA congruence criterion- Is he justified- Why or why not-

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Byju's Answer

Standard VIII

Mathematics

SAS Congruency Postulate

In ΔABC, ∠A=3...

Question

In $Δ A B C, ∠ A = 30^{\circ}, ∠ B = 40^{\circ} a n d ∠ C = 110^{\circ}$
In $Δ P Q R, ∠ P = 30^{\circ}, ∠ Q = 40^{\circ} a n d ∠ R = 110^{\circ}$
A student says that $Δ A B C ≅ Δ P Q R$ by AAA congruence criterion. Is he justified? Why or why not?

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Solution

No, because the two triangles with equal corresponding angles need not be congruent. In such a correspondence, one of them can be an enlarged copy of the other.

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Similar questions

Q. In

Δ A B C, ∠ A = 30^{\circ}, ∠ B = 40^{\circ} a n d ∠ C = 110^{\circ}

Δ P Q R, ∠ P = 30^{\circ}, ∠ Q = 40^{\circ} a n d ∠ R = 110^{\circ}

A student says that

Δ A B C ≅ Δ P Q R

by AAA congruence criterion. Is he justified? Why or why not?

In ΔABC, ∠A = 30°, ∠B = 40° and ∠C = 110°

In ΔPQR, ∠P = 30°, ∠Q = 40° and ∠R = 110°

A student says that ΔABC ≅ ΔPQR by AAA congruence criterion. Is he justified? Why or why not?

Question 4
In $Δ A B C, ∠ A = 30^{\circ}, ∠ B = 40^{\circ} a n d ∠ C = 110^{\circ}$
In $Δ P Q R, ∠ P = 30^{\circ}, ∠ Q = 40^{\circ} a n d ∠ R = 110^{\circ}$
A student says that $Δ A B C ≅ Δ P Q R$ by AAA congruence criterion. Is he justified? Why or why not?

Q. In

Δ A B C, ∠ A = 30^{o}, ∠ B = 40^{o}

and

∠ C = 110^{o}

Δ P Q R, ∠ P = 30^{o}, ∠ Q = 40^{o}

and

∠ R = 110^{o}

Then Is

Δ A B C ≅ Δ P Q R

by AAA ?

In $Δ$ ABC $\sim$ $Δ$ PQR by AAA criteria and $∠ B = ∠ R = 60^{\circ}$ . Find $∠$ RPQ.

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

No, because the two triangles with equal corresponding angles need not be congruent. In such a correspondence, one of them can be an enlarged copy of the other.

In $Δ A B C, ∠ A = 30^{\circ}, ∠ B = 40^{\circ} a n d ∠ C = 110^{\circ}$
In $Δ P Q R, ∠ P = 30^{\circ}, ∠ Q = 40^{\circ} a n d ∠ R = 110^{\circ}$
A student says that $Δ A B C ≅ Δ P Q R$ by AAA congruence criterion. Is he justified? Why or why not?