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Congruence of Triangles and Inequalities in a Triangle — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsCongruence of Triangles and Inequalities in a Triangle1 Mark
Question
It is given that$\triangle\text{ABC}\cong\triangle\text{FDE}$ in which AB = 5cm, $\angle\text{B}=40^{\circ},\angle\text{A}=80^{\circ}$and FD = 5cm. Then, which of the following is true?
  1. $\angle\text{D}=60^{\circ}$
  2. $\angle\text{E}=60^{\circ}$
  3. $\angle\text{F}=60^{\circ}$
  4. $\angle\text{D}=80^{\circ}$
✓

Answer

  1. $\angle\text{E}=60^{\circ}$

Solution:

Given $\triangle\text{ABC}\cong\triangle\text{FDE}$

$\angle\text{A}=\angle\text{F}=80^{\circ}$ ...(C.P.C.T.)

$\angle\text{B}=\angle\text{D}=40^{\circ}$ ...(C.P.C.T.)

$\angle\text{A}+\angle\text{B}+\angle\text{C}=180^{\circ}$ ...(Angle sum property)

$\Rightarrow80^{\circ}+40^{\circ}+\angle\text{C}=180^{\circ}$

$\Rightarrow\angle\text{C}=60^{\circ}$

$\therefore\angle\text{E}=\angle\text{C}=60^{\circ}$

$\therefore\angle\text{E}=60^{\circ}$

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