Question

If the side lengths \[AB=DE,BC=EF\] and \[DC=EF\], then \[\Delta ABC\_\_\_\_\_\_\_\Delta DEF\] .
\[\begin{align}
  & A)\cong \\
 & B)\approx \\
 & C)\ne \\
 & D)> \\
\end{align}\]

Answer 1

Hint: First of all, we have to understand the concept of congruence. By using the concept of Side-Side-Side congruency, if 3 sides in one triangle are equal to the corresponding 3 sides of a second triangle, then the triangles are congruent. The symbol of congruence is \[\cong \]. From the question, we are having a relation between the 3 sides of \[\Delta ABC\] and \[\Delta DEF\]. By using this concept, we can find the relation between them.

Complete step-by-step solution:
Before solving the question, we should know the concept of congruence and its properties. Two triangles are said to be congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure. There are 4 tests of measures for congruence Side-Side-Side, Side-Angle-Side, Angle-Side-Angle, and Angle-Angle-Side.
From the question we have that,
\[\begin{align}
  & AB=DE \\
 & BC=EF \\
 & AC=DF \\
\end{align}\]

From the Side – Side – Side congruence property it is clear that if 3 sides in one triangle are equal to the corresponding 3 sides of the second triangle, then the triangles are said to be congruent. The symbol of congruence is \[\cong \].
So, it is clear that \[\Delta ABC\cong \Delta DEF\]
Hence, we can say that option (A) is correct.

Note: We know that the congruence symbol is \[\cong \]. Some students may have a misconception and they may assume that the congruence symbol is \[\approx \]. If this misconception is followed, the answer will be \[\Delta ABC\approx \Delta DEF\]. But we know that \[\Delta ABC\cong \Delta DEF\]. So, it is clear that the answer is wrong. So, this misconception should be avoided by students.