Question

The measurements of ONLY ONE of the triangles shown above can be correct. Which one is it? (REMEMBER, the figures are NOT to scale)

Answer 1

Answer:

C) Reasons given below

Step-by-step explanation:

Theorems used :-  

1) Sum of two sides in a triangle should be greater than  one side.

2) Base angles in an isosceles triangle are equal.

3) Sum of all angles in a triangle should be 180° .

A) Consider a triangle with vertices A,B and C.(Image attached)

   Now if BA = BC then  

∠A = ∠C = 60°

[Since sum of all angles in a triangle is 180°,And one angle is  60°(Given) .So sum of other two sides = 120.And 120/2 = 60°]

∠A = ∠B = ∠C

It cannot be A since if all angles are equal then it cannot be a isosceles triangle.

Theorem 2 used.

B)

2.5cm + 3.5cm = 6cm

So, It cannot be a triangle.

Theorem 1 used.

D)

   100° + 55° +35°  = 190° ≠ 180°

Theorem 3 used .

C)

 6 + 4.5 > 7.5

 4.5 + 7.5 > 6

  6 + 7.5 > 4.5

Therefore Triangle C can be a triangle.

So the only answer can be C.

Hope it helps :)