Math  /  Geometry

QuestionIn triangles ABC and PQR,AB=AC,C=P\mathrm{PQR}, \mathrm{AB}=\mathrm{AC}, \angle \mathrm{C}=\angle \mathrm{P}, and B=Q\angle \mathrm{B}=\angle \mathrm{Q} then, the two triangles are: a) Isosceles and congruent b) Only Isosceles c) Only Congruent d) none of these

Studdy Solution
Since ABC\triangle \mathrm{ABC} and PQR\triangle \mathrm{PQR} have equal corresponding sides and angles, the two triangles are congruent by SAS or SSS criteria and isosceles by definition.
ABCPQRandABC and PQR are isosceles \triangle \mathrm{ABC} \cong \triangle \mathrm{PQR} \quad \text{and} \quad \triangle \mathrm{ABC} \text{ and } \triangle \mathrm{PQR} \text{ are isosceles}
The correct answer is: a) Isosceles and congruent

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