Question

please answer the image

Answer 1

Since, ∆ABC = ∆FDE

1. Angle A=80° & B =40°(given) , AB= 5cm
2. therefore, Angle C=180-(80°+40°)=60°
3. so, Angle D, F & E respectively are 40°, 80° & 60° and DF=5cm[because,∆ABC=∆FDE]
4. so, the answer is, (b)DF=5cm, angle E=60°

Answer 2

${\huge{\pink{\underline{\underline{Answes}}}}}$

• $\sf{Option = (b) DF = 5cm \:and ∠E = 60°}$

Explaining ;

GIVEN ;

$\sf{In \:the \:given \:∆ABC = \:∆FDE}$

• $\sf{AB = 5cm}$
• $\sf{∠B = 40°}$
• $\sf{∠A = 80°}$

TO FIND ;

$\sf{\:To \:find \:the \:true \:statement}$

Now;

$~~~~~~~\sf{:⇢DF = AB}$

$\sf{:⇢DF = 5cm}$$\sf\red{(\therefore by \:CPCT)}$

$~~~~~~~\sf{:⇢∠E = ∠C}$

$\sf{:⇢∠E = ∠C = 180° - (∠A° + ∠B°)}$$\sf\blue{(\therefore \:by \:angle \:sum \:property)}$

$\sf{:⇢∠E = 180° - (∠80° + ∠40°)}$

$\sf{:⇢∠E = 180° - (120°)}$

$\sf{:⇢∠E = 60°}$

So ; DF = 5cm ∠E = 60°

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$\sf\purple{CPCT}$ = CPCT stands for Corresponding parts of Congruent triangles. CPCT theorem states that if two or more triangles which are congruent to each other are taken then the corresponding angles and the sides of the triangles are also congruent to each other.