CAT Congruence of Triangles MCQ - Practice Questions & Answers

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Congruence of Triangles

You must have observed that two copies of your photographs of the same size are identical. Similarly, two bangles of the same size, two ATM cards issued by the same bank are identical. You may recall that on placing a one rupee coin on another minted in the same year, they cover each other completely.

Do you remember what such figures are called? Indeed they are called congruent figures (‘congruent’ means equal in all respects or figures whose shapes and sizes are both the same)

For congruence, we use the symbol $'{\color{Blue} \cong}\;'$ .

Congurent triangles: Two triangles are congruent if and only if one of them can be made to superpose on the other so as to cover it exactly.

Thus, congruent triangles are exactly identical.

Illustration 1: If $\triangle A B C \cong \triangle D E F$ then we have

$\angle A=\angle D, \angle B=\angle E, \angle C=\angle F \\ \text { and } A B=D E, B C=E F, A C=D F$

Illustration 2: If $\triangle A B C \cong \triangle FDE$ then we have

$\angle A=\angle F, \angle B=\angle D, \angle C=\angle E \\ \text { and } A B=FD, B C=DE, A C=E F$

Properties of Congruency in Triangle:

${\color{DarkBlue} (i)\text{ Every triangle is congruent to itself, i.e., }\triangle A B C \cong \triangle A BC.}$

${\color{DarkBlue} \text { (ii) If } \triangle A B C \cong \triangle D E F \text { then } \triangle D E F \cong \triangle A B C.}$

${\color{DarkBlue} \text { (iii) If } \triangle A B C \cong \triangle D E F, \text { and } \triangle D E F \cong \triangle P Q R \text { then } \triangle A B C \cong \triangle P Q R.}$