Question

Given two triangles $\Delta ABC$ and $\Delta DEF$ such: $BC=6\text{cm},AC=4\text{cm},m\angle B={35}^{\circ },$
$EF=6\text{cm},DF=4\text{cm},m\angle E={35}^{\circ }$, then $\Delta ABC\cong \Delta DEF$

• A. True.
• B. False

Answer 1

The correct option is B False

Given two triangles $\Delta ABC$ and $\Delta DEF$ with the given information:
$BC=6\text{cm},AC=4\text{cm},m\angle B={35}^{\circ },$
$EF=6\text{cm},DF=4\text{cm},m\angle E={35}^{\circ }$

Here, we can not apply SAS rule because equal angle i.e. ${35}^o$ is not included between equal sides here.

Here, If we draw the diagrams for both the triangles, we see the following two cases:
Clearly as $\angle C$ is not fixed, we can have the above two orientations both satisfying the given condition.

$\therefore$ We can't say for sure that the two triangles will be congruent.