Question

(a) If all the sides of a triangle are equal to the sides of another triangle, will both the triangles be congruent to each other?

(b) If AB is parallel to CD then $△$ABO should be congruent to $△$CDO always. Is this right? [2 MARKS]

Answer 1

Reason: 1 Mark each

(a)If three sides of one triangle are equal to the three sides of the other triangle, then the two triangles are congruent to each other by SSS congruence criterion.
$\Rightarrow$ Both triangles look like the mirror image of each other.
$\Rightarrow$ Both the triangles superimpose on each other.

So, if the sides of a triangle are congruent to the sides of another triangle, the two triangles will be congruent.

(b) Nothing is given or can be said about any of the corresponding sides in this case, As, AAA is not a rule for congruency, the triangles formed may or may not be congruent, depending on if the corresponding parts are equal or not.