Question

Which of the two triangles have \[\angle B\]common?

Answer 1

Hint: We write all the possible triangles that can be seen or formed in the given figure. Select two triangles that have \[\angle B\]as one of their angles.
* A triangle is a figure that has 3 vertices which on joining give us three sides. Each vertex has an angle associated with it.
* Common angle means the angle that exists in both the triangles.

Step-By-Step answer:
We are given the figure

Since there are four points in the figure i.e. A, B, C and D then the number of triangles is greater than one.
We write all possible triangles that can be formed using the given figure
\[\vartriangle ABC;\vartriangle ABD;\vartriangle ACD\]
So there are in total three triangles that can be formed using the given figure
Now we check in which of the two triangles from the three triangles formed we have angle B
In \[\vartriangle ABC\], we have angles A, B and C … (1)
In \[\vartriangle ABD\], we have angles A, B and D … (2)
In \[\vartriangle ACD\], we have angles A, C and D … (3)
Then from equations (1) and (2) we can see that angle B is existing in both triangles \[\vartriangle ABC\] and \[\vartriangle ABD\]

\[\therefore \]Two triangles having \[\angle B\] common are \[\vartriangle ABC\] and \[\vartriangle ABD\].

Note: Many students get confused with the given figure as they see it only as one triangle and write the answer as \[\vartriangle ABC\] and \[\vartriangle ACB\] by replacing the vertices in the name which is wrong. These two triangle names are for the same triangle, we use the line AD and write the two triangles formed by that line and then choose the triangles with common angle B.