Question

There is a unique quadrilateral ABCD possible with AB = 4 cm, BC = 6 cm, AC = 7 cm, CD = 5 cm and BD = 8 cm. State True or False.

• A. True
• B. False

Answer 1

The correct option is A

True

You don't need to draw the full quadrilateral you just need to know the basic property of triangles - "The sum of the lengths of any two sides of a triangle is always more than the third side.” Every quadrilateral is made of two triangles.

So if we can construct two triangles, we can construct the full quadrilateral. Here is a rough diagram of quadrilateral ABCD.

We have measures of AB, BC, AC, CD and BD. Also condition for constructing a triangle holds for $\Delta ABC$ and $\Delta BDC$. Thus, we can construct the quadrilateral ABCD.