Question

In the figure given above, AC is the diameter. AB, BC, AD, DC are chords of the circle.

AD = BC = 3 cm.

Then, $\Delta ABC\cong \Delta ADC$

• A. True
• B. False

Answer 1

The correct option is A

True

As the angles made by the diameter at the circumference is ${90}^{\circ }$, so $\Delta ABC$ and $\Delta ADC$ are right angle triangles, right angled at B and D respectively.

In the figure given above, consider

$\begin{array}{cc}& \\ In\Delta ABC& In\Delta ADC\\ A{B}^2+B{C}^2=A{C}^2& A{D}^2+D{C}^2=A{C}^2\\ A{B}^2+3^2=5^2& 3^2+D{C}^2=5^2\\ A{B}^2+25-9& 9+C^2=25\\ A{B}^2=16& D{C}^2=25-9\\ A{B}^2=4^2& D{C}^2=16\\ AB=4& DC=4\end{array}$

In $\Delta ABC$ and $\Delta ADC$
BC = AD (given)
AB = DC (AB = DC = 5 cm)
AC = AC (common side)
$\therefore \Delta ABC\cong ADC$ (by SSS criterion of congruency)