Properties of rhombuses

Learning Objectives Define a rhombus and identify its key properties. Apply the properties of rhombus diagonals to find unknown lengths and angles. Use the fact that all four sides of a rhombus are congruent to solve for variables and calculate perimeter. Prove that a given quadrilateral is a rhombus using its properties. Apply the Pythagorean theorem and trigonometric ratios to solve complex problems involving rhombuses. Calculate the area of a rhombus using its diagonals. Ever looked at a perfectly cut diamond or a classic kite? 💎 The secret to their symmetrical beauty lies in the properties of a special quadrilateral called a rhombus! In this tutorial, we will explore the unique characteristics of the rhombus, a special type of parallelogram. You will learn how its side...

TermDefinitionExample RhombusA quadrilateral with all four sides of equal length. A rhombus is also a type of parallelogram.A quadrilateral ABCD where AB = BC = CD = DA is a rhombus. DiagonalA line segment that connects two non-consecutive vertices of a polygon.In rhombus ABCD, the line segments AC and BD are the diagonals. Perpendicular BisectorA line that divides another line segment into two equal parts at a 90-degree angle.The diagonals of a rhombus are perpendicular bisectors of each other. Angle BisectorA line or ray that divides an angle into two congruent (equal measure) angles.In a rhombus, each diagonal bisects a pair of opposite angles. CongruentHaving the exact same size and shape. Represented by the symbol ≅.In rhombus PQRS, side PQ ≅ side QR.

Perpendicular Diagonals Property If ABCD is a rhombus, its diagonals AC and BD are perpendicular. AC \perp BD. This property means the diagonals intersect to form four right angles (90°). This is crucial for applying the Pythagorean theorem and trigonometry within the rhombus. Diagonal Angle Bisector Property If ABCD is a rhombus, diagonal AC bisects \angle DAB and \angle BCD, and diagonal BD bisects \angle ADC and \angle CBA. Use this rule when you know one of the main angles of the rhombus and need to find the smaller angles created by the diagonals, or vice-versa. Area Formula for a Rhombus Area = \frac{d_1 \times d_2}{2} To find the area of a rhombus, multiply the lengths of the two diagonals (d₁ and d₂) and then divide by 2. This is often more direct than using...