Mathematics
You have been given following specification regarding a quadrilateral. Measure of all the four angles and the length of one side is given. Would you be able to construct a unique quadrilateral in this case? Justify your answer.
Answer
No, we cannot construct a unique quadrilateral with only the measures of all four angles and the length of just one side.
In any quadrilateral, the sum of interior angles is always 360°. So even if all four angles are given, they only tell you the shape’s turning, not its exact size or proportions.
Knowing the length of only one side fixes the scale along that side, but the other sides can still vary.
Therefore, the given information is insufficient, and a unique quadrilateral cannot be constructed.
Related Questions
The diagonals of a quadrilateral intersect at right angles and it has exactly one axis of symmetry. The quadrilateral is a :
square
rhombus
kite
none of these
Which of the following quadrilaterals can you construct if you know the length of its diagonals?
Parallelogram
Rectangle
Rhombus
Square
ABCD is a rectangle in which diagonal BD bisects ∠B. Can we definitely say that ABCD is a square?