## Related questions with answers

Building Quadrilaterals Now use strands of spaghetti to conduct this quadrilateral-building experiment at least three times. Keep a record of your findings, including sketches of the shapes you make.

- Mark any three points along the length of a strand of spaghetti and break the spaghetti at those three points.
- Try to build a quadrilateral with the pieces end-to-end.
- If a quadrilateral can be built, try to build another, differently shaped quadrilateral with the same side lengths.

a. Was it possible to build a quadrilateral in each case? If a quadrilateral could be built, could you build a differently shaped quadrilateral using the same four segments? Compare your findings with those of others.

b. If a quadrilateral can be built from four side lengths, how are the side lengths related? Use a ruler and compass to test your conjecture for segments of length $3 \mathrm{~cm}, 5 \mathrm{~cm}, 8 \mathrm{~cm}$, and $10 \mathrm{~cm}$. For segments of length $4 \mathrm{~cm}, 4 \mathrm{~cm}, 7 \mathrm{~cm}$, and $15 \mathrm{~cm}$. For segments of length $2 \mathrm{~cm}, 4 \mathrm{~cm}, 8 \mathrm{~cm}$, and $16 \mathrm{~cm}$.

c. Suppose $a, b, c$, and $d$ are consecutive side lengths of any quadrilateral. Write an equation or inequality relating $a, b, c$, and $d$. How many different equations or inequalities can you write relating $a, b, c$, and $d$ ?

d. Write in words the relationship that must be satisfied by the four side lengths of any quadrilateral (do not use letters to name side lengths).

Special Quadrilaterals Quadrilaterals are more complicated than triangles. They bremore sides and more angles you discovered that using the ume four side lengths of a quadrilateral, you could build quite different shapes. Qudriaterals are classified as convex - as in the case of the quadrilateral below on thlefi-or nonconvex-as in the case of the quadrilateral on the right.

Solution

Verified### Part (a)

No! It was not possible to build a quadrilateral in each case.

yes! The shape was unique in each case.

All the students have same finding.

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