Lenths of the 2 shortests sides added together has to be greater than length of the longest side.
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You look at the lengths of the sided of the triangle. If the two lengths are same, the triangle is an isosceles triangle. If all the lengths are same, the triangle is an equilateral triangle. If none of the lengths are same, the triangle is a scalene triangle.
You'd have to know some relationship, formula, equation etc. among the angles and the lengths. There would be many relationships to choose from if the items you mention are the parts of a triangle, but if they are, you've kept it a secret.
A triangle (as you may know) by definiition has 3 sides; if you add up the lengths of all 3 sides, that total is called the perimeter.
You would have to consider a triangle formed by one diagonal and two sides of the quadrilateral. If you know the lengths of these sides, and the measure of the angle between them, you can use the cosine law to find the diagonal. c2 = a2 + b2 -2ab(cosC)
You can't. You must know at least one length and at least two angles, or vice versa.