Free printable resources · Original practice
Plot the vertices in order, close the shape and use parallel sides, equal sides and diagonal symmetry to identify the quadrilateral family.
Free quadrilateral drawing worksheets with rectangles, parallelograms, trapezoids and kites. Letter/A4 reference and answer files included.
Choose Letter or A4, then download a student sheet first. Keep the separate reference or answer file closed until you have attempted the case. Every worksheet, SVG and answer is free without signup.
Original worksheet collection. Letter or A4 PDF and editable SVG.
Original worksheet collection. Letter or A4 PDF and editable SVG.
Original worksheet collection. Letter or A4 PDF and editable SVG.
Original worksheet collection. Letter or A4 PDF and editable SVG.
Complete free PDF pack.
| Case | Given information | Task |
|---|---|---|
| QU01 | Vertices in order: A(0, 0); B(5, 0); C(5, 3); D(0, 3). | Plot and join the vertices. Classify using parallel or equal sides and calculate area. Here trapezoid means exactly one parallel pair. |
| QU02 | Vertices in order: A(0, 0); B(5, 0); C(7, 3); D(2, 3). | Plot and join the vertices. Classify using parallel or equal sides and calculate area. Here trapezoid means exactly one parallel pair. |
| QU03 | Vertices in order: A(0, 0); B(6, 0); C(4, 3); D(1, 3). | Plot and join the vertices. Classify using parallel or equal sides and calculate area. Here trapezoid means exactly one parallel pair. |
| QU04 | Vertices in order: A(0, 3); B(2, 0); C(4, 3); D(2, 7). | Plot and join the vertices. Classify using parallel or equal sides and calculate area. Here trapezoid means exactly one parallel pair. |
Use the coordinates, dimensions and rules given for each case. Distances and areas are measured in grid units.
QU01: Rectangle
| Step | Worked result |
|---|---|
| 1 | Classification: rectangle. Parallel opposite-side pairs: 2. |
| 2 | Squared side lengths: 25, 9, 25, 9. Area = 15 square units. |
The first case shows the checking pattern. Individual answer files contain the completed graph or net and result for every case.
Plot each vertex in order and join consecutive points. Two pairs of parallel opposite sides identify a parallelogram; equal opposite side lengths alone do not prove that it is a rectangle. To identify a rectangle, also check that adjacent sides meet at right angles. A trapezoid here has exactly one parallel pair. A kite here has two distinct pairs of equal adjacent sides. Use squared lengths to compare sides without square roots. For A(0,0), B(5,0), C(5,3), D(0,3), alternate sides are horizontal and vertical, so all angles are right; the area is 5 × 3 = 15 square units.
After plotting, compute area using the coordinate grid. For rectangles and parallelograms, area equals base times height. For the trapezoid, use the average of the parallel sides times the height. For the kite, use half the product of the diagonals. In the supplied cases: rectangle area 15; parallelogram area 15; trapezoid area 27/2; kite area 14. For the kite, diagonals AC = 4 and BD = 7, so area = (4 × 7)/2 = 14. Keep exact fractions where given; do not round 27/2 to a decimal unless asked.
For nonvertical lines, parallel lines have equal slopes and different intercepts. Perpendicular lines have slopes whose product is -1. A product of 1 does not indicate parallel lines. Vertical and horizontal lines are perpendicular even though the slope product is undefined. Equal slopes with equal intercepts describe the same line, not two parallel lines. When classifying quadrilaterals, verify both parallel pairs and side lengths; slope product alone only tests perpendicularity, so it cannot establish parallelism.
| Watch for | Check instead |
|---|---|
| Assuming equal slopes always mean parallel lines. | Equal slopes with equal intercepts describe the same line. Parallel lines require equal slopes and different intercepts. |
| Using slope product 1 to test for parallel lines. | For nonvertical lines, parallel lines have equal slopes. A slope product of -1 tests perpendicularity, not parallelism. |
| Classifying a kite as having parallel sides. | In this worksheet, a kite has two distinct pairs of adjacent equal sides and no parallel sides. The supplied kite example has zero parallel pairs. |
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Count parallel opposite-side pairs. This worksheet defines a trapezoid as having exactly one parallel pair. If there are two parallel pairs, classify as a parallelogram or rectangle instead.
Squared lengths avoid square roots and still show equality. For example, squared lengths 25, 9, 25, 9 indicate opposite sides equal. Compare squared values directly when checking side equality.
For the kite with vertices A(0,3), B(2,0), C(4,3), D(2,7), diagonals AC = 4 and BD = 7. Area equals half the product of the diagonals: (4 × 7)/2 = 14 square units.
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