Learn about the different types and properties of quadrilaterals.
Example 1: What is a Quadrilateral?
Understand the definition and basic components of a quadrilateral.
Definition: A quadrilateral is a polygon with four sides and four vertices (corners).
Sides and Vertices: A quadrilateral has four line segments as its sides and four points as its vertices.
Angles: A quadrilateral has four interior angles.
Angle Sum Property: The sum of the interior angles of any quadrilateral is always 360 degrees.
If the angles are A, B, C, and D, then Angle A + Angle B + Angle C + Angle D = 360 degrees.
Diagonals: A line segment connecting two non-adjacent vertices is called a diagonal. A quadrilateral has two diagonals.
Example 2: Types of Quadrilaterals
Explore different classifications of quadrilaterals based on their properties.
Parallelogram: A quadrilateral with both pairs of opposite sides parallel.
Rectangle: A parallelogram with four right angles.
Square: A rectangle with four equal sides. (A square is also a rhombus).
Rhombus: A parallelogram with four equal sides.
Trapezoid (or Trapezium): A quadrilateral with at least one pair of parallel sides.
Kite: A quadrilateral with two distinct pairs of equal-length sides that are adjacent to each other.
Example 3: Properties of a Parallelogram
Learn the key properties that define a parallelogram.
Property 1: Opposite sides are parallel (by definition). AB || DC and AD || BC in parallelogram ABCD.
Property 2: Opposite sides are congruent (equal in length). AB = DC and AD = BC.
Property 3: Opposite angles are congruent (equal in measure). Angle A = Angle C and Angle B = Angle D.
Property 4: Consecutive interior angles are supplementary (sum to 180 degrees). Angle A + Angle B = 180, Angle B + Angle C = 180, etc.
Property 5: The diagonals bisect each other (they cut each other in half at their intersection point). If diagonals AC and BD intersect at O, then AO = OC and BO = OD.
Example 4: Angle Sum Property Application
Find a missing angle in a quadrilateral using the angle sum property.
Property: The sum of the interior angles of any quadrilateral is 360 degrees.
Example Problem: In quadrilateral ABCD, Angle A = 80 degrees, Angle B = 100 degrees, Angle C = 70 degrees. Find Angle D.
Step 1: Use the Angle Sum Property: Angle A + Angle B + Angle C + Angle D = 360 degrees.
Step 2: Substitute the given values into the equation.
80 + 100 + 70 + Angle D = 360.
Step 3: Sum the known angles.
250 + Angle D = 360.
Step 4: Solve for Angle D.
Angle D = 360 - 250.
Step 5: Calculate the value of Angle D.
Angle D = 110 degrees.
Result: The measure of Angle D is 110 degrees.
Practice Mode - Parallelogram Side Checker
Enter the lengths of the four sides of a quadrilateral to check if it could be a parallelogram.
Note: Enter the side lengths in order around the quadrilateral (e.g., side1, side2, side3, side4) separated by commas.
Related Concepts
Explore these related geometrical concepts.
Polygon
A closed figure made of straight line segments.
Vertex
A corner point of a polygon.
Diagonal
A line segment connecting non-adjacent vertices.
Parallel Lines
Lines in the same plane that never intersect.
Congruent
Having the same size and shape.
Supplementary Angles
Two angles whose sum is 180 degrees.
Rectangle
A parallelogram with four right angles.
Square
A rectangle with four equal sides.
Rhombus
A parallelogram with four equal sides.
Trapezoid
A quadrilateral with at least one pair of parallel sides.
Kite
A quadrilateral with two pairs of adjacent equal sides.