Question

(a) Find all the angles of a right-angled isosceles triangle.
(b) Is a triangle ABC with side length AB = 12 cm, BC = 8 cm and AC = 20 cm possible? Explain why. [3 MARKS]

Answer 1

(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 and AC = 20 cm is not possible because in a triangle the 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.