Learn the precise steps to construct quadrilaterals using only a ruler and compass — no protractor needed for many of them.
A quadrilateral has 4 sides and 4 angles — 8 measurements total, but you only need 5 independent pieces of information (like 4 sides and 1 diagonal, or other combinations) to construct it uniquely, since a quadrilateral can be split into two triangles.
Why can 5 measurements uniquely determine a quadrilateral?
Because a quadrilateral splits into two triangles along a diagonal, and each triangle needs 3 measurements, but they share one side (the diagonal), so 3+3−1 = 5 measurements are needed
What are common sets of 5 measurements used to construct a quadrilateral?
4 sides and 1 diagonal, or 3 sides and 2 diagonals, or 2 sides and 3 angles, among other valid combinations
To construct a quadrilateral given 4 sides and a diagonal, first construct one triangle using the diagonal and two sides, then construct the second triangle on the other side of that same diagonal using the remaining two sides.
If you know sides AB, BC, CD, DA, and diagonal AC of quadrilateral ABCD, what's the first triangle you'd construct?
Triangle ABC, using sides AB, BC, and diagonal AC
After constructing triangle ABC, how do you complete the quadrilateral?
Using the same diagonal AC, construct triangle ACD using sides CD and DA, on the other side of AC from B
1. How many independent measurements are needed to construct a unique quadrilateral?
2. Name a set of 5 measurements that can be used to construct a quadrilateral.
3. If a quadrilateral is split into two triangles by a diagonal, how many total sides do the two triangles have (counting the shared diagonal twice)?
4. Why must the two triangles share the diagonal exactly, rather than each having their own separate diagonal length?
5. If you're given all 4 sides of a quadrilateral but no diagonal or angle, can you construct a unique quadrilateral?