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Triangles — MATHS STD 7 — Question

Gujarat BoardEnglish MediumSTD 7MATHSTriangles3 Marks
Question
In Figure. $\angle1=\angle2$ and $\angle3=\angle4.$
  1. Is $\triangle\text{ADC}\cong\triangle\text{ABC}?$ why$?$
  2. Show that $AD = AB$ and $CD = CB.$
✓

Answer

  1. In $\triangle\text{ADC}$ and $\triangle\text{ABC},$
$\angle1=\angle2$ [given]
$\text{AC}=\text{AC}$ [common side]
$\angle3=\angle4$ [given]
By $ASA$ congruence criterion, $\triangle\text{ADC}\cong\triangle\text{ABC}$
  1. $\text{AD} = \text{AB} [$by $CPCT]$
$\text{CD} = \text{CB} [$by $CPCT]$

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