Question

Given below are pairs of congruent triangles. State the property of congruence and name the congruent triangles in each case.
(i)

(ii)

(iii)

(iv)

(v)

Answer 1

(i)Given

From above figure, we observe that
$BC=EF,AC=ED$ and $\angle C=\angle E$
Thus, by SAS property, we say that
$\Delta ACB\cong \Delta DEF$
(ii) Given

From above figure, we observe that $RQ=ML$, $QP=MN$ and $\angle P=\angle N$
Thus, by SAS property we say that
$\Delta RPQ\cong \Delta LNM$(RHS congruence property)
(iii) Given

From above figure, we observe that $ZY=TS$, $XZ=RS$ and $XY=RT$
Thus, by SSS property we say that
$\Delta YXZ\cong \Delta TRS$
(iv)Given

From above figure, we observe that
$\angle F=\angle M,\angle E=\angle N$ and $EF=MN$
Thus, by ASA property, we say that
$\Delta DEF\cong \Delta PNM$
(v) Given

From above figure, we observe that
$\angle BAC=\angle CAD$
$AC=AC$ (common side)
$\angle BCA=\angle DCA$
Thus, by ASA property we say that,
$\Delta ACB\cong \Delta ACD$