Question

Which condition of congruence proves that the following pair of triangles are congruent.

A. RHS
B. SSS
C. ASA
D. SAS

Answer 1

Hint: This question is based on congruence of two triangles. First step is to look for equal angles and equal sides in the two triangles. Here two angles and one side of one triangle is equal to that of another. So we will look for ASA rules of congruence.

Complete step-by-step answer:
In the question two right triangles are given and also it is given that they are congruent and we have to just find which congruence condition holds here.
We know that two triangles are said to be congruent if the corresponding sides and corresponding angles of one triangle is equal to that of another triangle.
It means the two triangles are equal in all aspects.
 Also we know that two triangles are congruent by ASA method if:
(i) Two angles made on the same side of one triangle is equal to that of another triangle.
(ii) The side on which the two angles are made is equal for both triangles.

The diagram for the question is given as:

Now we will write down the equality of angles and sides of two triangles which is given in the diagram.
It is given that in $\vartriangle {\text{ABC}}$ and$\vartriangle {\text{EFG}}$:
$\angle {\text{ABC = }}\angle {\text{EFG}}$
    BC = FG
and $\angle {\text{BCA = }}\angle {\text{FGA}}$
 Here we can see that:
(i) Two angles made on the same side of one triangle is equal to that of another triangle.
(ii) The side on which the two angles are made is equal for both triangles i.e. BC= FG
Therefore we can say that the two given triangles are congruent to each other by ASA rule of congruence.
So option C is correct.

Note: In this type of question, you should know the meaning of congruent triangles and also the rules of congruence of two triangles. Different rules of congruence are:
(i) SSS - All sides of one triangle are equal to the corresponding sides of the other triangle.
(ii) RHS- In right triangles, one side and hypotenuse are equal.
(iii)SAS- Two sides and one angle between two sides are equal