"If two sides and an angle of one triangle are equal to two sides and an angle of another triangle,then the two triangles must be congruent." Is the statement true? Why?
(B) The statement is false. For two triangles to be congruent by the $SAS$ (Side-Angle-Side) congruence rule,the angle must be the included angle between the two sides. If the angle is not the included angle,the triangles are not necessarily congruent.
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Similar Questions
In triangles $ABC$ and $PQR$,$\angle A = \angle Q$ and $\angle B = \angle R$. Which side of $\triangle PQR$ should be equal to side $AB$ of $\triangle ABC$ so that the two triangles are congruent? Give reason for your answer.
Easy
View SolutionIn the given figure,if $PQ = ST$,$QU = TR$,$PQ \perp QT$ and $ST \perp TQ$,then prove that $PR = SU$.
Medium
View Solution$PL, QM$ and $RN$ are the altitudes of $\Delta PQR$. If $PL = QM = RN$,then by $RHS$ criterion of congruence,prove that $\Delta PQR$ is an equilateral triangle.
Medium
View SolutionIn the given figure,$l \parallel m$ and $M$ is the mid-point of a line segment $AB$. Show that $M$ is also the mid-point of any line segment $CD,$ having its end points on $l$ and $m,$ respectively.
Medium
View Solution$E$ and $F$ are respectively the mid-points of equal sides $AB$ and $AC$ of $\Delta ABC$ (see figure). Show that $BF = CE$.
Easy
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