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Questions and Answers
All quadrilaterals are parallelograms.
All quadrilaterals are parallelograms.
False (B)
All parallelograms are quadrilaterals.
All parallelograms are quadrilaterals.
True (A)
A square is a parallelogram.
A square is a parallelogram.
True (A)
A parallelogram with a right angle is a square.
A parallelogram with a right angle is a square.
All rectangles are parallelograms.
All rectangles are parallelograms.
All rhombuses are squares.
All rhombuses are squares.
All squares are rectangles.
All squares are rectangles.
A parallelogram with 4 congruent sides is a square.
A parallelogram with 4 congruent sides is a square.
A parallelogram with 4 perpendicular diagonals is a rhombus.
A parallelogram with 4 perpendicular diagonals is a rhombus.
A trapezoid cannot be a parallelogram.
A trapezoid cannot be a parallelogram.
All parallelograms with perpendicular angles are kites.
All parallelograms with perpendicular angles are kites.
All rectangles are squares.
All rectangles are squares.
A parallelogram with 4 congruent sides is a rhombus.
A parallelogram with 4 congruent sides is a rhombus.
All squares are rectangles.
All squares are rectangles.
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Study Notes
Quadrilaterals Overview
- Non omnes quadrilaterals es parallelograms; solum parallelograms sunt un subtype de quadrilateral.
- Omnes parallelograms, tamen, sunt quadrilaterals per definitionem.
Properties of Parallelograms
- Un quadrato es un parallelogram: habet pares lateres paralelli et angulos rectos.
- Un parallelogramma cum angulo recto non est semper un quadrato, nam potestas laterum non est restricta ad congruentiam.
Special Types of Parallelograms
- Omnes rectanguli sunt parallelograms, sed non omnes parallelograms sunt rectanguli; rectanguli habent angulos rectos.
- Non omnes rhombuses sunt quadrati; a rhombus definitorium habet lateres congruentes, sed non necessitate angulos rectos.
- Un parallelogramma cum quattuor lateribus congruentibus non est semper un quadrato, si anguli non sunt recti.
Diagonal Properties
- Un parallelogramma cum diagonales perpendiculares est definitorie un rhombus; omnes rhombuses habent diagonales qui se intersecte in angulos rectos.
Distinctions of Shapes
- Un trapezoidum non potest esse un parallelogram; trapezoida definitorie habent tantum un par laterum paralellorum.
- Non omnes parallelograms cum angulis perpendiculares sunt kites, quia kites habent etiam proprietatem de lateribus congruentibus.
Recap of Squares
- Omnes quadrati sunt rectanguli, sed non omnes rectanguli sunt quadrati; quadrati habent omnes lateres et angulos aequales.
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