Concept:A triangle can be uniquely constructed when its side lengths or a combination of sides and angles are fixed. Having only three angles gives many similar triangles of different sizes.
Explanation:Given two angles and one side (option A): Draw the side. At its ends, draw the two given angles. The rays intersect to form the third vertex. So a triangle can be built.
Given only three sides (option B): Draw one side. Draw arcs of the other two sides from its ends. The arc intersection gives the third point. A unique triangle is formed.
Given only three angles (option C): You get the shape but not the size. Triangles with the same angles are similar, so you cannot fix a specific triangle. Construction is not possible.
Given two sides and the included angle (option D): Draw one side. From the endpoint, draw the given angle and the second side. Join the free ends. A unique triangle results.
Answer:C. only three angles
