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Congruence — MATHS STD 7 — Question

Gujarat BoardEnglish MediumSTD 7MATHSCongruence2 Marks
Question
In Figure, $\ce{AB = DC}$ and $\ce{BC = AD}$.
$i.$ Is $\triangle\text{ABC}\cong\triangle\text{CBD}?$
$ii.$ What congruence condition have you used?
$iii.$ You have used some fact, not given in the question, what is that?
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Answer

We have $\ce{AB = DC}$
$\ce{BC = AD}$
And $\ce{AC = AC}$
$i.$ Yes by $\ce{SSS}$ $\triangle\text{ABC}\cong\triangle\text{CBD}$
$ii.$ We have used Side congruence condition with one side common in both the triangles.
$iii.$ Yes, have used the fact that $\ce{AC = CA}.$

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