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Congruence — Maths STD 7 — Question

Maharashtra BoardEnglish MediumSTD 7MathsCongruence4 Marks
Question
In figure, AB || DC and AB = DC.
  1. Is $\triangle\text{ACD}\cong\triangle\text{CAB}?$
  2. State the three pairs of matching parts used to answer (i).
  3. Which angle is equal to $\angle\text{CAD}?$
  4. Does it follow from (iii) that AD || BC?
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Answer

  1. Yes by SAS condition of congruency, $\triangle\text{DCA}\cong\triangle\text{BAC}$.
  2. We have used AB = DC, AC = CA and $\angle\text{DCA}=\angle\text{BAC}$.
  3. $\angle\text{CAD}=\angle\text{ACB}$ since the two triangles are congruent.
  4. Yes this follows from AD || BC as alternate angles are equal. lf alternate angles are equal the lines are parallel.

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