Question : If in $\triangle \mathrm{ABC}$ and $\triangle \mathrm{DEF}, \frac{A B}{D E}=\frac{B C}{F D}$, then they will be similar when:
Option 1: $\angle B=\angle D$
Option 2: $\angle A=\angle D$
Option 3: $\angle A=\angle F$
Option 4: $\angle B=\angle E$
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Correct Answer: $\angle B=\angle D$
Solution :
$\frac{AB}{DE} = \frac{BC}{FD}$ ⇒ $\frac{AB}{BC} = \frac{DE}{FD}$ Angle between $AB$ and $BC$ is $\angle B$ and angle between $DE$ and $FD$ is $\angle D$. $\therefore$ They will be similar when these angles will be equal, i.e, $\angle B = \angle D$ Hence, the correct answer is $\angle B = \angle D$.
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Question : If it is given that for two right-angled triangles $\triangle$ABC and $\triangle$DFE, $\angle$A = 25°, $\angle$E = 25°, $\angle$B = $\angle$F = 90°, and AC = ED, then which one of the following is TRUE?
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Question : For congruent triangles $\triangle$ABC and $\triangle$DEF, which of the following statements is correct?
Question : $\triangle \mathrm{ABC}$ is a right-angle triangle at $\mathrm{B}$. If $\tan \mathrm{A}=\frac{5}{12}$, then $\sin \mathrm{A}+\sin \mathrm{B}+\sin \mathrm{C}$ will be equal to:
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