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Is AAS congruence criterion the same as ASA congruence criterion?

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True

False

answer is B.

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Detailed Solution

Consider the two triangles as shown in the below figure,
seo

Consider we are given that,
∠B=∠Q
∠C=∠R
AC=PR
Using angle sum property in ΔABC,
∠A+∠B+∠C=

180^{\circ}

∠A +

40^{\circ}

80^{\circ}

180^{\circ}

∠A =

60^{\circ}

Similarly using angle sum property in ΔPRQ,
∠P+∠Q+∠R =

180^{\circ}

∠P +

40^{\circ}

80^{\circ}

180^{\circ}

∠P =

60^{\circ}

Now in ΔABC and ΔPQR,
∠A = ∠P (both

60^{\circ}

)
AC = PR (given)
∠C = ∠R (both

80^{\circ}

)
Hence ΔABC ≅ ΔPQR (ASA congruence rule)
In ΔABC and ΔPQR,
∠B = ∠Q (both

40^{\circ}

)
∠C = ∠R (both

80^{\circ}

)
AC = PR (given)
Hence ΔABC ≅ ΔPQR (AAS congruence rule)
Hence, we can see that the conditions that we used to prove both triangles congruent by ASA and AAS method are different.
So, the given statement is false.

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