In triangles ABC and PQR, AB = AC, ∠C = ∠P and ∠B = ∠Q. The two triangles are ___. isosceles but not congruent isosceles and congruent congruent but not isosceles neither congruent nor isosceles

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In triangles ABC and PQR, AB = AC,  ∠C =  ∠P and  ∠B =  ∠Q. The two triangles are ___. isosceles but not congruent isosceles and congruent congruent but not isosceles neither congruent nor isosceles

Cayden Hull · Accepted Answer

The correct option is  D isosceles but not congruent  ∠A+ ∠B+ ∠C =  ∠P+ ∠Q+ ∠R But,  ∠C = ∠P and  ∠B = ∠Q ----(1)  ∠A+ ∠B+ ∠C =  ∠C+ ∠B+ ∠R Therefore,  ∠A = ∠R△ABC ≈  △PQR (AAA similarity) As AB = AC,  △ABC is an isosceles triangle.∠B = ∠C (opposite angles of equal sides)∠P = ∠Q△PQR is isosceles.The relation between sides of the 2 triangles is not known, congruency between the 2 triangles either by SAS or ASA cannot be proved.△ABC and △PQR are similar and isosceles triangles.

In triangles ABC and PQR, AB = AC, ∠C = ∠P and ∠B = ∠Q. The two triangles are ___. isosceles but not congruent isosceles and congruent congruent but not isosceles neither congruent nor isosceles

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