AAS(or SAA) test:State whether the given statement is True or False.Statement: The sum of the measures of angles in a triangle is 1800. Therefore, if two corresponding pairs of angles in two triangles are congruent, then the remaining pair of angles is also congruent. Hence if two angles and a side adjacent to one of them are congruent with corresponding parts of the other triangle then the condition for ASA test is fulfilled. So, the triangles are congruent.

Question

AAS(or SAA) test:State whether the given statement is True or False.Statement: The sum of the measures of angles in a triangle is 1800. Therefore, if two corresponding pairs of angles in two triangles are congruent, then the remaining pair of angles is also congruent. Hence if two angles and a side adjacent to one of them are congruent with corresponding parts of the other triangle then the condition for ASA test is fulfilled. So, the triangles are congruent.

Accepted Answer

Let us take the two triangles ΔABC, ΔDEF as shown in below figure
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⇒ From the above triangles
⇒ Length of BC = a
⇒ Length of AC = b
⇒ Length of AB = c
⇒ Length of EF = d
⇒ Length of DF = e
⇒ Length of DE = f
⇒ The angle ∠BAC = α
⇒ The angle ∠ABC = β
⇒ The angle ∠ACB = γ
⇒ The angle ∠EDF = δ
⇒ The angle ∠DEF = ε
⇒ The angle ∠DFE = ζ
Given that, the sum of all the measures of the angles in a triangle is

180^{0}

, then
α + β + γ =

180^{0}

and δ + ε + ζ =

180^{0}

Now the sum of all the angles in the two triangles is
α + β + γ + δ + ε + ζ =

180^{0}

+

180^{0}

=

360^{0}

If α = δ = x and β = ε = y then the values of γ , ζ are
γ =

180^{0}

− (α + β) and ζ =

180^{0}

− (δ + ε)
Substituting the values of α,β,δ,ε in the above equations then we have
γ =

180^{0}

− (x + y) and
ζ =

180^{0}

− (x + y)
= γ
Now let us compare the two triangles
We have
α = δ β = ε
Then automatically γ = ζ
⇒ And AB = pDE [Where p is the constant]
⇒ We know that in two triangles the two angles and one corresponding side is equal/congruent to the corresponding angles and side in another triangle then the two triangles are congruent to each other on the Side Angle Angle rule.
⇒ So, the correct option is (1)
Hence, the given statement is true.

AAS(or SAA) test:

State whether the given statement is True or False.

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