"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
Write the measures of the sides of $\Delta PQR$ in ascending order,given that $\angle P = 40^{\circ}$ and $\angle R = 80^{\circ}$.
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 SolutionState whether the following statement is true or false:
$(1)$ $\angle ABD$ and $\angle ACE$ are the exterior angles of $\Delta ABC$. If $\angle ABD = 110^{\circ}$ and $\angle ACE = 130^{\circ}$,then $AB > AC$.
$(1)$ $\angle ABD$ and $\angle ACE$ are the exterior angles of $\Delta ABC$. If $\angle ABD = 110^{\circ}$ and $\angle ACE = 130^{\circ}$,then $AB > AC$.
Easy
View Solution$ABC$ is an isosceles triangle in which $AC = BC$. $AD$ and $BE$ are respectively two altitudes to sides $BC$ and $AC$. Prove that $AE = BD$.
Medium
View Solution$ABC$ is a right-angled triangle with $AB = AC$. The bisector of $\angle A$ meets $BC$ at $D$. Prove that $BC = 2 AD$.
Difficult
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