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Congruence — Maths STD 7 — Question

Maharashtra BoardEnglish MediumSTD 7MathsCongruence3 Marks
Question
In Figure, AB = AD and $\angle\text{BAC}=\angle\text{DAC}$.
  1. State in symbolic form the congruence of two triangles ABC and ADC that is true.
  2. Complete each of the following, so as to make it true:
  1. $\angle\text{ABC}$ =
  2. $\angle\text{ACD}$ =
  3. Line segment AC bisects and .
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✓

Answer

  1. AB = AD (given)
$\angle\text{BAC}=\angle\text{DAC}$ (given)
AC = CA (common)
Therefore by SAS condition of congruency, $\triangle\text{ABC}\cong\triangle\text{ADC}$
  1.  
  1. $\angle\text{ABC}=\angle\text{ADC}$ (c.p.c.t)
  2. $\angle\text{ACD}=\angle\text{ACB}$ (c.p.c.t)
  3. Line segment AC bisects AD and AB.

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