Answer:
:
(a) Answer: 1 Mark
(b) Answer: 1 Mark
Reason: 1 Mark
(a) In a right-angled isosceles triangle, sides other than the hypotenuse are equal in length.
In ABC, AB = BC $\Rightarrow \angle 1=\angle 3$ -------------------I
By angle sum property of triangle,
$\angle 1+\angle 2+\angle 3={180}^{\circ }$
$\angle 1+90+\angle 1={180}^{\circ }$
$2\angle 1={90}^{\circ }$
$\Rightarrow \angle 1={45}^{\circ }=\angle 2$
So, angles are ${45}^{\circ },{45}^{\circ }and{90}^{\circ }$
(b)A triangle ABC with the given side lengths of AB = 12 cm, BC = 8 cm andAC = 20 cm is not possible becausein a trianglethe sum of any two sides should be greater than the third side but in this triangle, AB + BC = 20 cm which is equal to the third side AC = 20 cm. AB + BC should have been greater than AC.