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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Standard VII

Mathematics

SAS Criteria for Congruency

In ABC , ∠ A ...

Question

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?

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Solution

No. This property represents that these triangles have their respective angles of equal measure. However, this gives no information about their sides. The sides of these triangles have a ratio somewhat different than 1:1. Therefore, AAA property does not prove the two triangles congruent.

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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?

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 $△$ ABC, $∠ A = 30^{o}$ , $∠ B = 40^{o}$ and $∠ C = 110^{o}$

In $△$ PQR, $∠ P = 30^{o}$ , $∠ Q = 40^{o}$ and $∠ R = 110^{o}$ .

Then the two triangles are necessarily congruent.

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. This property represents that these triangles have their respective angles of equal measure. However, this gives no information about their sides. The sides of these triangles have a ratio somewhat different than 1:1. Therefore, AAA property does not prove the two triangles congruent.

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?