Properties of quadrilaterals (Review)

Learning Objectives Identify and classify different types of quadrilaterals based on their properties. Recall and apply the properties of sides, angles, and diagonals for parallelograms, rectangles, rhombuses, squares, trapezoids, and kites. Solve for unknown side lengths, angle measures, and diagonal lengths in various quadrilaterals. Differentiate between quadrilaterals by comparing and contrasting their unique and shared properties. Use the properties of quadrilaterals to set up and solve algebraic equations. Apply the properties of quadrilaterals as foundational knowledge for geometric proofs. Ever noticed the shapes in a honeycomb or a tiled floor? 🐝 Why do some four-sided shapes fit together perfectly while others don't? This tutorial is a comprehensive review o...

TermDefinitionExample ParallelogramA quadrilateral with two pairs of parallel opposite sides. Key properties include: opposite sides are congruent, opposite angles are congruent, and diagonals bisect each other.A standard playing card that has been tilted. RectangleA parallelogram with four right angles. Its diagonals are congruent and bisect each other.The screen of your phone or a standard door frame. RhombusA parallelogram with four congruent sides. Its diagonals are perpendicular bisectors of each other and they bisect the angles of the rhombus.The classic 'diamond' shape in a deck of cards. SquareA parallelogram that is both a rectangle and a rhombus. It has four congruent sides and four right angles. Its diagonals are congruent, perpendicular, and bisect each other.A face...

Interior Angle Sum of a Quadrilateral \angle A + \angle B + \angle C + \angle D = 360^{\circ} The sum of the measures of the four interior angles of any convex quadrilateral is always 360 degrees. This is fundamental for finding unknown angles. Properties of Parallelogram Diagonals If diagonals AC and BD intersect at E, then AE = EC and BE = ED. The diagonals of any parallelogram cut each other into two equal halves. This property is often used to find lengths or prove that a shape is a parallelogram. Midsegment of a Trapezoid M = \frac{1}{2}(b_1 + b_2) The midsegment of a trapezoid connects the midpoints of the non-parallel sides. Its length is the average of the lengths of the two parallel bases (b1 and b2).