Answer to Question #207895 in Geometry for KoralAnnaki

Question

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

Answer 1

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 $\Delta ABC$ and $\Delta PQR$ are equilateral

then

$\angle A \approx\angle P=60\degree\\\angle B\approx\angle Q=60\degree\\\angle C\approx\angle R=60\degree$

But they have different lengths

AB=a and PQ=b

$a\mathrlap{\,/}{=}b\\AB\mathrlap{\,/}{=}PQ$

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