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Congruence — Maths STD 7 — Question

Maharashtra BoardEnglish MediumSTD 7MathsCongruence2 Marks
Question
$\triangle\text{ABC}$ and $\triangle\text{ABD}$ are on a common base AB, and AC = BD and BC = AD as shown in Figure. Which of the following statements is true?
  1. $\triangle\text{ABC}\cong\triangle\text{ABD}$
  2. $\triangle\text{ABC}\cong\triangle\text{ADB}$
  3. $\triangle\text{ABC}\cong\triangle\text{BAD}$
✓

Answer

In $\triangle\text{ABC}$ and $\triangle\text{BAD}$ we have,
AC = BD (given)
BC = AD (given)
and AB = BA (common)
Therefore, by SSS criterion of congruency, $\triangle\text{ABC}\cong\triangle\text{BAD}$
There option (iii) is true.

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