Mathematics
Grade 10
15 min
Properties of rhombuses
Properties of rhombuses
What you'll learn
- Calculate the product of three or more numbers, including one decimal number, with at least 80% accuracy on a worksheet containing 10 problems.
- Explain the steps involved in multiplying three numbers when one of them is a decimal to a partner, using correct mathematical vocabulary (factor, product, decimal place).
- Solve word problems involving the multiplication of three or more numbers, including one decimal, and correctly identify the required operation in at least 3 out of 4 problems.
- Estimate the product of three or more numbers, one of which is a decimal, before calculating the exact answer and explain if your final answer is reasonable based on your estimate.
Tutorial Preview
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Introduction & Learning Objectives
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...
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Key Concepts & Vocabulary
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.
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Core Formulas
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...
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Challenging
The area of a rhombus is 144 square units. The length of one diagonal is twice the length of the other. What is the perimeter of the rhombus?
A.12√5 units
B.24√5 units
C.48 units
D.60 units
Challenging
The side length of a rhombus is 8 cm and one of its interior angles is 120°. What is the area of the rhombus?
A.16√3 cm²
B.32 cm²
C.32√3 cm²
D.64 cm²
Challenging
A quadrilateral has vertices at A(1, 4), B(5, 6), C(9, 4), and D(5, 2). Which statement best describes this quadrilateral?
A.It is a rhombus but not a square.
B.It is a square.
C.It is a kite but not a rhombus.
D.It is a parallelogram but not a rhombus.
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Frequently asked questions
What grade level is "Properties of rhombuses"?
Properties of rhombuses is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Properties of rhombuses?
You'll be able to: Calculate the product of three or more numbers, including one decimal number, with at least 80% accuracy on a worksheet containing 10 problems; Explain the steps involved in multiplying three numbers when one of them is a….
Is "Properties of rhombuses" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Properties of rhombuses?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.