Question

Are these pairs of triangles congruent ?
In each case state the condition of congruency in \[\Delta ABC\] and \[\Delta QRP\] , \[AB = QR\], \[\angle B = \ \angle R\] and \[\angle C = \ \angle P\]

Answer 1

Hint: In this question, we need to check whether the \[\Delta ABC\] and \[\Delta QRP\] are congruent or not. First, we need to draw a figure according to the given information. Then we need to find the similarities among both triangles. If the similarities of both the triangles turn out to be true, then we can say that the given two triangles are congruent to each other.

Complete step-by-step answer:
Here we need to find whether the given triangles are congruent or not.
Given, \[\Delta ABC\] and \[\Delta QRP\] , \[AB = QR\], \[\angle B = \ \angle R\] and \[\angle C = \ \angle P\] .
First, We can draw their figures according to the information provided.

Now on applying, AAS congruence criteria on the triangles ABC and QRP.
1 . \[\angle B = \ \angle R\] (given)
2. \[\angle C = \ \angle P\] (given)
3. \[AB = QR\] (given)
Thus it is clear that the \[\Delta ABC\] and \[\Delta QRP\] are congruent by angle-angle-side postulates.
Thus \[\Delta ABC\ \cong \Delta QRP\]
Final answer :
The \[\Delta ABC\] and \[\Delta QRP\] are congruent.

Note: For solving this problem we need to know about the Congruence of the triangles . Two triangles are said to be congruent to each other if all three corresponding sides are equal and all the three corresponding angles are equal in measure. We also need to know that there are four ways to find the congruence between the two triangles. They are SSS postulate where SSS stands for side-side-side , SAS postulate where SAS stands for side-angle-side, ASA postulate where ASA stands for angle-side-angle and AAS postulate where AAS stands for angle-angle-side.