Question

If \[\Delta ABC \cong \Delta XYZ\]then find which side of\[\Delta XYZ\] is congruent to \[BC\].

Answer 1

Hint: Two triangles are equivalent if their corresponding sides are equal in length and their corresponding angles are equal in measure.
If is \[\Delta ABC\] congruent to \[\Delta XYZ\], the relationship can be written mathematically as
\[\Delta ABC \cong \Delta XYZ\]
In \[\Delta ABC\] and \[\Delta XYZ\] their corresponding sides are equal in length and their corresponding angles are equal in measure.
Congruent to one another is nothing but the shape of one of the triangles can be formed from another by doing turns, flips etc.

Complete answer:.
It is given that, \[\Delta ABC \cong \Delta XYZ\]
That is \[\Delta ABC\] and \[\Delta XYZ\] are congruent to each other.
It means that one shape can become another using turns, flips and/or slides.
Let us carry out the process of turning, flipping or sliding. The graphical explanation is given below,
Rotation:

Reflection:

Translation:

When two triangles are congruent they will have exactly the same three sides and exactly the same three angles by the definition of congruence.
 It is given that \[\Delta ABC \cong \Delta XYZ\] then by the property of congruence of triangles.
The corresponding sides in both the triangles are,
\[AB \cong XY\]
Also we get,
\[BC \cong YZ\]
The final corresponding side in the triangle is,
\[CA \cong ZX\]
Our main task in the problem is to find the side corresponding to the side \[BC\] in the \[\Delta ABC\].
Since,\[BC \cong YZ\] we can come to a conclusion that \[BC\] is congruent to the side \[YZ\].
Hence, the side \[YZ\] is congruent to \[BC\].

Note:
Two triangles are congruent; they will have exactly the same three sides and exactly the same three angles. In this question we use the concept of rotation, reflection and translation to understand the meaning of congruent.