Question #207895

Sketch a counterexample showing that each statement is false:


1) Two triangles with three pairs of congruent angles must also have three pairs of congruent sides


1
Expert's answer
2021-06-18T07:03:06-0400

The statement is completely FALSE

Two triangles with three pairs of congruent angles are not neccessarily required to have three pairs of congruent sides.

Example:-

Let ΔABC\Delta ABC and ΔPQR\Delta PQR are equilateral

then

AP=60°BQ=60°CR=60°\angle A \approx\angle P=60\degree\\\angle B\approx\angle Q=60\degree\\\angle C\approx\angle R=60\degree


But they have different lengths

AB=a and PQ=b

a/=bAB/=PQa\mathrlap{\,/}{=}b\\AB\mathrlap{\,/}{=}PQ





Both triangles have pairs of congruent angles but not pairs of congruent sides


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