Prove the following theorem:
If the angle between the vectors $\vec a$ and $\vec b$ is not greater than 90 degrees then the length of the vector ($\vec a + \vec b)$ is not less than $\vec a$ or $\vec b$.
The theorem is in the part where only vector addition is introduced so would appreciate if someone can post a solution involving only summing vectors. Otherwise any other solution is welcome. I tried using triangle inequality/law of cosines but they both involve vector products.
PS: Constructing random vectors it seems to be that the smaller the angle the smaller the sum of the two vectors is going to be.