Question

State the correspondence between the vertices, sides and angles of the following pairs of congruent triangles.
(a) $\Delta PQR\cong \Delta ABC$
(b) $\Delta XYZ\cong \Delta MNO$

Answer 1

Hint: We know that two triangles are congruent if the sides and angles of one triangle are equal to the corresponding sides and angles of another triangle. The order of letters in the name of two triangles will indicate the correspondence between the vertices, angles and sides of two triangles.

Complete step by step answer:
We need to find the correspondence between the vertices, sides and angles of the given pairs of congruent triangles. We know that two triangles are congruent if the sides and angles of one triangle are equal to the corresponding sides and angles of another triangle. Let us consider each section of the question.
(a) Let us first find the correspondence between the vertices, sides and angles of $\Delta PQR\text{ and }\Delta ABC$ .
Correspondence between the vertices can be given as:
$P\leftrightarrow A,Q\leftrightarrow B,R\leftrightarrow C$
We can write the correspondence between the sides as:
$\begin{align}
  & PQ=AB \\
 & QR=BC \\
 & PR=AC \\
\end{align}$
Now, let us state the correspondence between the angles.
$\begin{align}
  & \angle P=\angle A \\
 & \angle Q=\angle B \\
 & \angle R=\angle C \\
\end{align}$
This can be clearly seen from the following figure.

(b) Let us now find the correspondence between the vertices, sides and angles of $\Delta XYZ\cong \Delta MNO$ .
Correspondence between the vertices can be given as:
$X\leftrightarrow M,Y\leftrightarrow N,Z\leftrightarrow O$
We can write the correspondence between the sides as:
$\begin{align}
  & XY=MN \\
 & YZ=NO \\
 & XZ=MO \\
\end{align}$
Now, let us state the correspondence between the angles.
$\begin{align}
  & \angle X=\angle M \\
 & \angle Y=\angle N \\
 & \angle Z=\angle O \\
\end{align}$
This can be clearly seen from the following figure.

Note:
We must be aware that the correspondence between vertices, sides and angles are applicable only when the two triangles are congruent. The order of letters in the name of two triangles will indicate the correspondence between the vertices of two triangles.