The measurements of ONLY ONE of the triangles shown above can be corre

1.	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» 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 :)

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»

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.

2.5cm + 3.5cm = 6CM

So, It cannot be a triangle.

Theorem 1 used.

100° + 55° +35° = 190° ≠ 180°

Theorem 3 used .

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 :)