Question

in a given figure if ×> y then prove that MP > NP...... Help plizzzzzzzzzzzzzzzz ​

Answer 1

Solution:-

Given:

1. A triangle with exterior angles x and y.
2. ∠x > ∠y

To prove:

• MP > NP

Proof:

Given,

➡ ∠x > ∠y

Multiplying both sides by -1, We get,

➡ -∠x < -∠y

Adding 180° to both sides, We get,

➡ 180° - ∠x > 180° - ∠y

From figure,

180° - ∠x = ∠PMN and 180° - ∠y = ∠PNM

Therefore,

➡ ∠PMN < ∠PNM

We know that,

1. The longest side of a triangle is opposite to the longest angle and,
2. The shortest side of a triangle is opposite to the shortest angle.

Here, ∠PMN is opposite to NP.

Also, ∠PNM is opposite to MP.

So,

➡ NP < MP

➡ MP > NP (Hence Proved)