Question

For the following congruent triangles, find the pairs of corresponding angles.

Answer 1

Hint:Here we have to find the pairs of corresponding angles in the given two congruent triangles. Here we have \[\Delta POQ\] and \[\Delta ROS\]. We use one of the four rules used to prove whether a given set of triangles are congruent. That is by SSS rule, SAS rule, ASA rule and AAS rule.

Complete step by step answer:
Congruent triangles are triangles that have the same size and shape. This means that the corresponding sides are equal and the corresponding angles are equal. There are four rules used to prove whether a given set of triangles are congruent. The four rules are the SSS rule, SAS rule, ASA rule and AAS rule.

Side-Angle-Side (SAS) rule statement: If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent. Side-Side-Side (SSS) rule states that: If three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.

Angle-Side-Angle (ASA) rule states that: If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent. Angle-Angle-Side (AAS) rule states that: If two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, then the triangles are congruent.

To say the triangles are congruent using the SAS Postulate, if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. By SAS congruent rule
In \[\Delta POQ\] and \[\Delta ROS\]
\[PO = 4\,cm = RO\]
\[\Rightarrow OQ = 4\,cm = OS\]
\[\Rightarrow PQ = 5\,cm = RS\]
\[ \Rightarrow \]\[\Delta POQ \cong \Delta ROS\]
\[ \Rightarrow \]\[\angle OPQ = \angle ORS\]
\[\Rightarrow \angle POQ = \angle ROS\]
\[\therefore \angle PQO = \angle RSO\]

Note:As long as one of the four rules is true, it is sufficient to prove that the two triangles are congruent. An included angle is an angle formed by two given sides. In general we know that if two triangles are congruent they will have exactly the same three sides and the same three angels. But similar triangles are different from congruent triangles. Similar triangles will have the same shape but their size may vary.