Questions and Answers
What are the properties of a parallelogram?
What is a parallelogram?
A quadrilateral in which two pairs of opposite sides are parallel.
Which property is not true for all parallelograms?
Diagonals of a rectangle are always congruent.
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A rectangle must be a parallelogram.
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Which figure does not always have congruent diagonals?
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What is a rhombus?
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A quadrilateral whose diagonals bisect each other and are perpendicular is a _____.
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If the diagonals of a quadrilateral do not bisect each other, what could the quadrilateral be?
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What defines an isosceles trapezoid?
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What is the difference between a parallelogram and a trapezoid?
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Study Notes
Properties of a Parallelogram
- Opposite sides are parallel and congruent.
- Opposite angles are congruent while adjacent angles are supplementary.
- Diagonals bisect each other and create two congruent triangles.
Parallelogram Definition
- A quadrilateral with two pairs of opposite sides that are parallel.
Properties of a Rectangle
- Shares all properties of a parallelogram.
- All four angles are right angles (90°).
- Diagonals are congruent, dividing the rectangle into four isosceles triangles.
Rectangle Definition
- A specific type of parallelogram that contains at least one right angle.
Properties of a Rhombus
- Shares all properties of a parallelogram.
- All four sides are congruent and consecutive sides are equal.
- Diagonals are perpendicular and bisect the angles from which they are drawn.
Rhombus Definition
- A parallelogram with two congruent consecutive sides.
Properties of a Square
- Shares all properties of both a rectangle and a rhombus.
- All four sides are congruent and all angles are right angles.
- Diagonals are congruent, perpendicular, and bisect the angles.
Square Definition
- A specific type of rectangle that has two congruent consecutive sides.
Parallelogram vs Rectangle
- Both have opposite sides that are parallel and congruent, but rectangles must have right angles.
Key Statement about Parallelograms
- Diagonals are guaranteed to bisect each other in all parallelograms.
Diagonals of a Rectangle
- The diagonals of a rectangle are congruent and they bisect each other.
Congruent Diagonals in Parallelograms
- A parallelogram must be classified as a rectangle if its diagonals are congruent.
Non-Congruent Diagonals
- A rhombus does not always have congruent diagonals, unlike squares and rectangles.
Quadrilaterals Definition
- A shape with four sides and four angles.
Trapezoid Definition
- A quadrilateral with exactly one pair of parallel sides.
Isosceles Trapezoid Definition
- A special form of trapezoid where the non-parallel sides are equal in length.
Properties of an Isosceles Trapezoid
- Features one pair of parallel sides, congruent non-parallel sides, congruent base angles, and congruent diagonals.
- Opposite angles are supplementary, totaling 180°.
Diagonals in Quadrilaterals
- If the diagonals of a quadrilateral do not bisect each other, the shape could be a trapezoid.
Parallelogram vs Trapezoid
- Parallelograms have two pairs of parallel sides, whereas trapezoids have only one.
Perpendicular Diagonals in Rhombus
- A parallelogram qualifies as a rhombus if its diagonals are perpendicular to each other.
Non-Congruent Diagonals in a Parallelogram
- If the diagonals of a parallelogram are perpendicular but not congruent, the shape is classified as a rhombus.
Length in Rhombus
- The relationship between the lengths of the sides of a rhombus can be calculated using the formula (a^2 + b^2 = c^2).
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Test your understanding of the properties and definitions related to parallelograms with these helpful flashcards. This quiz covers essential geometric rules that are crucial for mastering the concepts of parallelograms in your geometry studies.
