Question

Two triangles are congruent to each other as given in the figure by RHS criteria, then choose the correct option(s).

• A. BC $\ne$ DE
• B. BC = DE
• C. DE = 4 cm
• D. $\angle$ B $\ne$ $\angle$ E

Answer 1

Answer: (B), (C)

The correct options are
B BC = DE
C DE = 4 cm

In the figure,
$△$ ABC $\cong$ $△$ DEF by RHS criteria
AC is hypotenuse of $△$ ABC
AB , BC are sides of $△$ ABC
$\angle$ B = ${90}^{\circ }$
and
DF is hypotenuse of $△$ DEF
DE , EF are sides of $△$ DEF
$\angle$ E = ${90}^{\circ }$

AB = 3 cm, EF = 3 cm
AC = 5 cm, DF = 5 cm

Applying pythagoras theorem in $\Delta$ DEF,
$D{F}^2=D{E}^2+E{F}^2$
$5^2=D{E}^2+3^2$
$25-9=D{E}^2$
$16=D{E}^2$
$DE=\sqrt{16}=4cm$

$\therefore$ AC = DF [Hypotenuse]
$\angle$ B = $\angle$ E = ${90}^{\circ }$
Now, BC = DE = 4 cm [ C.P.C.T]