Question

12) The difference of the lengths of any two sides of triangle is *
O A) greater
B)less
OC)equal to
O d
d) half of the third side​

Answer 1

Answer:

difference of any two sides of a triangle is less than to the third side.

Step-by-step explanation:

To prove: AC-AB< BC

Construction: Mark a point 'D' on AC such that the distance AB=AD

Therefore, we have to prove that AC-AD

So, we have to prove that CD < BC

Proof:

Consider triangle ABD,

since AB=AD

Since, opposite angles opposite to the equal opposite sides are always equal.

So,

So, p = p

Now, let

Now, using exterior angle property in triangle ABD,

Exterior angle property of a triangle states that the measure of an exterior angle is equal to the sum of the two interior angles.

(equation 1)

Now, using exterior angle property in triangle BCD,

(equation 2)

Now, by comparing equation 1 and 2,

So, y > x

BC > CD

CD < BC

AC - AD < BC

Since, AD = AB

Therefore, AC - AB < BC

Hence, proved.

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