Geometry - Quadrilaterals Flashcards
What is a Quadrilateral?
Four coplanar line segments linked end to end to create a closed figure.
A 4-sided polygon.
Also known as tetragon, quadrangle
What is a square?
A 4-sided regular polygon with all sides equal and all internal angles 90°
A square can be thought of as a special case of other quadrilaterals, for example
- a rectangle but with adjacent sides equal
- a parallelogram but with adjacent sides equal and the angles all 90°
- a rhombus but with angles all 90°
What is a rectangle?
A 4-sided polygon where all interior angles are 90°
Properties of a rectangle
- Opposite sides are parallel and congruent Adjust the rectangle above and satisfy yourself that this is so.
- The diagonals bisect each other
- The diagonals are congruent
What is a Parallelogram?
A quadrilateral with both pairs of opposite sides parallel.
A parallelogram is a quadrilateral with opposite sides parallel. But there are various tests that can be applied to see if something is a parallelogram.
It is the “parent” of some other quadrilaterals, which are obtained by adding restrictions of various kinds:
- A rectangle is a parallelogram but with all four interior angles fixed at 90°
- A rhombus is a parallelogram but with all four sides equal in length
- A square is a parallelogram but with all sides equal in length and all interior angles 90°
A quadrilateral is a parallelogram if:
- Both pairs of opposite sides are parallel. (By definition). Or:
- Both pairs of opposite sides are congruent. If they are congruent, they must also be parallel. Or:
- One pair of opposite sides are congruent and parallel. Then, the other pair must also be parallel.
What is a Trapezoid?
A quadrilateral which has at least one pair of parallel sides
(USA definition)
(but see definition notes below)
What is Rhombus?
A quadrilateral with all four sides equal in length.
A rhombus is actually just a special type of parallelogram. Recall that in a parallelogram each pair of opposite sides are equal in length. With a rhombus, all four sides are the same length.It therefore has all the properties of a parallelogram. See Definition of a parallelogram
Its a bit like a square that can ‘lean over’ and the interior angles need not be 90°. Sometimes called a ‘diamond’ or ‘lozenge’ shape.
What is a Kite?
A quadrilateral with two distinct pairs of equal adjacent sides.
A kite-shaped figure.
A kite is a member of the quadrilateral family, and while easy to understand visually, is a little tricky to define in precise mathematical terms. It has two pairs of equal sides. Each pair must be adjacent sides(sharing a common vertex) and each pair must be distinct. That is, the pairs cannot have a side in common.
What is a Polygon?
A number of coplanar line segments, each connected end to end to form a closed shape.
- Triangle - 3 sides
- Quadrilateral - 4 sides
- Tetragon - 4 sides
- Pentagon - 5 sides
- Hexagon - 6 sides
- Heptagon - 7 sides
- Octagon - 8 sides
- Decagon - 10 sides
- Dodecagon - 12 sides
What is a Congruent?
Equal in size and shape
Two objects are congruent if they have the same dimensions and shape. Very loosely, you can think of it as meaning ‘equal’, but it has a very precise meaning that you should understand completely, especially for complex shapes such as polygons.
Congruent line segments
Two line segments are congruent if they have the same length. But they need not lie at the same angle or position on the plane.
See Congruent Line Segments
Congruent angles
Two angles are congruent if they have the same measure. So if two separate angles have measures of 30° and 23° for example, they are not congruent because they have different measures. Congruent angles may lie in different orientations or positions. See Congruent Angles
Congruent circles
Two circles are congruent if they have the same size. The size can be measured as the radius, diameter or circumference. They can overlap.
Congruent polygons
Congruent polygons have an equal number of sides, and all the corresponding sides and angles are congruent. However, they can be in a different location, rotated or flipped over. So for example the two triangles shown on the right are congruent even though one is a mirror image of the other.
What is a circle?
A line forming a closed loop, every point on which is a fixed distance from a center point.
What is a diagonal?
A diagonal is a straight line drawn from one corner of a polygon to another. The corners must not be next each other.
What is reflection symmetry?
A shape has reflection symmetry if it can eb folded along a line so that one half fits exactly onto the other half. The line is called line of symmetry.
What is rotation symmetry?
A shape has rotation symmetry if it fits onto itself more than once when it is rotated 360o
The order or rotation symmetry is the number of times a shape fits onto itself when it is rotated 360o
