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Unit 5: Lesson 4

Topic D: Drawing, analysis, and classification of two-dimensional shapes

There are many different types of quadrilaterals. A quadrilateral is defined as a two-dimensional shape with four sides, four vertices, and four angles. There are two main types: concave and convex. There are also various subcategories of convex quadrilaterals, such as trapezoids, parallelograms, rectangles, rhombi, and squares. Created by Sal Khan.

Want to join the conversation?

• Does the sides have to be equal to be a quad.
(1 vote)
• not necessarily. the weird pink shape that he showed did not have equal sides
• It is and do quadrilaterals have to be closed?
• All polygons must be closed. In fact there are other rules. 1. polygons must be closed. 2. They must be composed of line segments (no curves) 3. No sides can intersect one another (except at the vertices) Hope this helps! :)
• How does a square go under the description of both the rectangle and rhombus? Is it because a square and a rectangle and rhombus all have 2 parallel sides? or is it because of something else?
• A rectangle has 4 straight sides and 4 right angles.

A rhombus must have opposite equal angles and 4 equal sides.

A square has 2 sets of opposite right angles and 4 straight, equal sides, so it fits into both categories.

Hope this helps!
• ¿Could a Perfect Hexagon be a parallelogram?
• Even though you may think there is another parallel side for each side in a regular hexagon, the definition of a parallelogram is a four-sided plane rectilinear figure with opposite sides parallel.

I hope this helped!
• It is and do quadrilaterals have to be closed?
• Yes, all polygons are defined as closed figures.
• Can someone give me an overview of the differences between Rhombi, Parallelograms and Rectangles?
• So you start with a parallelogram, two pairs of parallel sides, opposite sides are congruent, adjacent angles are supplementary, diagonals bisect each other, and opposite angles are congruent.
IF a parallelogram has an angle of 90 degrees (thus all 4 angles are 90) it is a rectangle - all rules of parallelograms apply plus diagonals are congruent.
IF a parallelogram has 4 equal sides, then it is a rhombus. All parallelogram rules apply plus the diagonals are perpendicular bisectors of each other.
IF it has both equal sides and all 90 degree angles, then it is a square which has all the properties of parallelograms, rhombii, and rectangles.
• I do not understand the difference between a quadrilateral, parallelogram, rhombus?
• Quadrilateral = 4 sides (4 angles, 4 vertices)
(concave is the one that is not convex and vice versa)
Trapezoid (restrictive classification) = convex quadrilateral + exactly 2 parallel sides
Parallelogram = convex quadrilateral + 2 pairs of parallel sides
Rectangle = convex quadrilateral + parallelogram + 4 angles of 90º
Rhombus = convex quadrilateral + parallelogram + 4 sides of the same size
Square = convex quadrilateral + parallelogram + rectangle + rhombus
• If a square can be a rectangle, can it be a rhombus?
• Yes. All squares are both rectangles and rhombi.