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Unit 8: Quadrilaterals and Polygons

Parallelograms, rectangles, rhombuses, and kites sorted into a family tree by which properties they do and don't share.

5 topics · 17 questions

Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.

Properties of Parallelograms

  1. How it worksHow does drawing one diagonal split a parallelogram into two congruent triangles?
  2. Worked exampleFind the missing angle of a parallelogram if one angle measures 65 degrees.
  3. Common mistakeWhy don't a parallelogram's diagonals have to be equal in length the way a rectangle's do?
  4. Going furtherWhat happens to a parallelogram's diagonals when it's reshaped into a rectangle?
Your turn1 of 2
One angle of a parallelogram measures 121 degrees. Find the measure of the angle right next to it (a consecutive angle).

Proving a Quadrilateral Is a Parallelogram

  1. How it worksHow do the five different ways to prove a parallelogram all guarantee opposite sides end up parallel?
  2. Worked exampleProve a quadrilateral with vertices (0,0), (4,0), (5,3), (1,3) is a parallelogram using its diagonals' midpoints.
  3. Common mistakeWhy doesn't having one pair of parallel sides alone make a quadrilateral a parallelogram?
Your turn1 of 2
A quadrilateral has vertices A(0, 0), B(11, 0), C(11 + 2, 14), and D(2, 14). Find the sum of the coordinates of the midpoint of diagonal AC, which must equal the midpoint of diagonal BD to prove ABCD is a parallelogram.

Rectangles, Rhombuses, and Squares

  1. How it worksHow do a rectangle's congruent diagonals and a rhombus's perpendicular diagonals combine to make a square's diagonals do both?
  2. Worked exampleFind the length of a rhombus's diagonal if its side is 10 and the other diagonal is 12.
  3. Common mistakeWhy isn't every rhombus automatically a square?
Your turn1 of 2
A rhombus has a side length of 17 and one diagonal of length 11. Find the length of the other diagonal.

Trapezoids and Kites

  1. How it worksHow do a kite's two pairs of consecutive congruent sides force its diagonals to be perpendicular?
  2. Worked exampleFind the length of the midsegment of a trapezoid with parallel sides of 8 and 14.
  3. Worked exampleFind the area of an isosceles trapezoid with parallel sides 6 and 12 and legs of length 5.
  4. Common mistakeWhy don't a trapezoid's legs have to be the same length unless it's specifically isosceles?
Your turn1 of 2
A trapezoid has parallel sides of length 15 and 14. Find the length of its midsegment.

The Quadrilateral Hierarchy

  1. How it worksHow do the nested categories of parallelogram, rectangle, rhombus, and square each add one more restriction?
  2. Common mistakeWhy doesn't having four equal sides automatically make a quadrilateral a square?
  3. Going furtherWhat happens to the hierarchy diagram if you add a shape with four equal angles but unequal sides?
Your turn1 of 2
Why doesn't having four equal sides automatically make a quadrilateral a square?