Question

why Is it possible to construct a quadrilateral from any 4 given measurements of its sides.​

Answer 1

Step-by-step explanation:

Suppose 2 sides and a diagonal forming a triangle having the three angles be x, y, z.

By sine rule we can find the three angles.

For one angle draw a perpendicular from the vertex of a triangle to the diagonal. This will give u a right angled triangle for which three sides are known and by trigonometry we can find the angles.

Now out of the three angles of the triangle we know one of the angle. By sine rule we can determine the remaining two angle.

Similarly we can draw another triangle with a diagonal, one remaining known side & one unknown side. For any quadrilateral, we know the opposite angles are congruent. We can have our one angle of this triangle.

Also opposite sides are parallel, then by alternate interior angles property, we can have the remaining the two angles of the triangle. Then by joining the 2 triangles we can have our quadrilateral for which we now know the four sides, the four angles & the two diagonals.

Answer 2

Answer:

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