Triangles Test - 7

They do not form an isosceles triangle as no two sides have same length.

Option B:

Take AB + BC = 5 + 12

= 17 > 15

Take AB + CA = 5 + 15

= 20 > 12

Take BC+CA = 12 + 15

= 27 > 5

In all the scenarios we can see that the sum of two sides is greater than the third side.

Option C:

Now,

AB² + BC² = 5² + 12²

= 25 + 144

= 169

CA² = 15²

= 225

As AB² + BC² ≠ CA²

These sides do not form a right-angle triangle.

Option D:

In the option B we can see that a triangle is formed, so option D is not correct.

Hence, option B is correct.

We know that the sum of two sides is greater than the third side.

Option A:

Take three sides as AB = 4 cm, BC = 2.5 cm, CA = 2.4 cm

AB + BC = 4 cm + 2.5 cm

= 6.5 cm > 2.4 cm

AB + CA = 4 cm + 2.4 cm

= 6.4 cm > 2.4 cm

BC + CA = 2.5 cm + 2.4 cm

= 4.9 cm > 4 cm

The property that the sum of two sides is greater than the third side is true in every scenario.

Option B:

Take three sides as AB = 4 cm, BC = 2.5 cm, CA = 2.6 cm

AB + BC = 4 cm + 2.5 cm

= 6.5 cm > 2.6 cm

AB + CA = 4 cm + 2.6 cm

= 6.6 cm > 2.5 cm

BC + CA = 2.5 cm + 2.6 cm

= 5.1 cm > 4 cm

The property that the sum of two sides is greater than the third side is true in every scenario.

Option C:

Take three sides as AB = 4 cm, BC = 2.5 cm, CA = 2.8 cm

AB + BC = 4 cm + 2.5 cm

= 6.5 cm > 2.8 cm

AB + CA = 4 cm + 2.8 cm

= 6.8 cm > 2.5 cm

BC + CA = 2.5 cm + 2.8 cm

= 5.3 cm > 4 cm

The property that the sum of two sides is greater than the third side is true in every scenario.

Option D:

Take three sides as AB = 4 cm, BC = 2.5 cm, CA = 1.1 cm

AB + BC = 4 cm + 2.5 cm

= 6.5 cm > 1.1 cm

AB + CA = 4 cm + 1.1 cm

= 5.1 cm > 2.5 cm

BC + CA = 2.5 cm + 1.1 cm

= 3.6 cm < 4 cm

The property that the sum of two sides is greater than the third side is not true in every scenario.

Hence, option D is correct.

All angles cannot be greater than 60° as it will give the sum of angles more than 180°.

Example:

Let ∠A = 65°, ∠ B = 110°, ∠C = 95°

Then,

∠A + ∠B + ∠ C = 65° + 110° + 95°

= 270°

Which is not possible.

So, option A is incorrect.

Option B:

All angles cannot be less than 60° as it will give the sum of angles less than 180°.

Example:

Let ∠A = 45°, ∠ B = 20°, ∠C = 35°

Then,

∠A + ∠B + ∠ C = 45° + 20° + 35°

= 100°

Which is not possible.

So, option B is incorrect.

Option C:

Let a triangle has 2 right angles.

So those two angles would add to 90+90 = 180 degrees.

But there are 3 angles to any triangle and they always add to 180 degrees.

If the first two add to 180 degrees, then the 3rd remaining angle must be 0 degrees, which doesn't make much sense.

So, this proves that a triangle cannot have two right angles.

So, option C is incorrect.

Option D:

An exterior angle is equal to the sum of the opposite interior angles. And we know a sum is always greater than the given numbers whose sum was taken.

It follows that it must be larger than either one of them.

So, option D is correct.

Hence, option D is correct.