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Questions and Answers
Which of the following are properties of a parallelogram? (Select all that apply)
Which of the following are properties of a parallelogram? (Select all that apply)
- Diagonals are perpendicular.
- Diagonals bisect each other. (correct)
- Opposite angles are congruent. (correct)
- Both pairs of opposite sides are congruent. (correct)
Which properties apply to a rectangle? (Select all that apply)
Which properties apply to a rectangle? (Select all that apply)
- Diagonals bisect each other. (correct)
- All sides are congruent.
- All angles are right angles. (correct)
- All properties of a parallelogram. (correct)
Which of the following are properties of a square? (Select all that apply)
Which of the following are properties of a square? (Select all that apply)
- All properties of a parallelogram. (correct)
- All properties of a rectangle. (correct)
- Diagonals are congruent.
- All properties of a rhombus. (correct)
Which of the following are properties of a rhombus? (Select all that apply)
Which of the following are properties of a rhombus? (Select all that apply)
What is a property of a trapezoid?
What is a property of a trapezoid?
What is the area formula for a rectangle?
What is the area formula for a rectangle?
What is the area formula for a trapezoid?
What is the area formula for a trapezoid?
What does the distance formula prove about a parallelogram?
What does the distance formula prove about a parallelogram?
What does the slope formula prove about a parallelogram?
What does the slope formula prove about a parallelogram?
What does the midpoint formula prove in relation to diagonals?
What does the midpoint formula prove in relation to diagonals?
What is the formula for the area of a square?
What is the formula for the area of a square?
What is unique about the legs of a trapezoid?
What is unique about the legs of a trapezoid?
What is a base in the context of a trapezoid?
What is a base in the context of a trapezoid?
Match the following shapes with their properties:
Match the following shapes with their properties:
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Study Notes
Properties of Parallelograms
- Opposite sides are congruent and parallel.
- Opposite angles are congruent.
- Consecutive angles are supplementary.
- Diagonals bisect each other.
- One pair of opposite sides can be both parallel and congruent.
Properties of Rectangles
- All parallelogram properties apply.
- All angles are right angles (90 degrees).
- Diagonals are congruent in length.
- Base angles are congruent.
Properties of Squares
- Includes all properties of parallelograms, rectangles, and rhombuses.
- All sides are congruent and angles are right angles.
Properties of Rhombuses
- All parallelogram properties apply.
- Diagonals are perpendicular to one another.
- Diagonals bisect opposite angles.
- All four sides are congruent.
Properties of Trapezoids
- Has one pair of parallel sides.
- Diagonals create two non-congruent triangles.
- Same side interior angles are supplementary.
Properties of Isosceles Trapezoids
- Diagonals are congruent.
- One pair of opposite sides is congruent.
- Base angles are congruent.
Properties of Kites
- One diagonal bisects the other.
- Diagonals meet at right angles.
- One diagonal creates two non-congruent triangles.
- Two distinct pairs of congruent consecutive sides exist.
Geometric Relationships
- Common properties of parallelogram, rhombus, rectangle, and square include diagonals bisecting each other and congruent opposite angles.
- Rectangles, squares, and isosceles trapezoids share congruent base angles and congruent diagonals.
- Same side interior angles are supplementary across several quadrilaterals, including trapezoids and isosceles trapezoids.
Area Formulas
- Area of a rectangle: ( l \times w )
- Area of a square: ( s^2 ) or ( \frac{1}{2}(d_1 \times d_2) )
- Area of a parallelogram: ( b \times h )
- Area of trapezoid: ( \frac{1}{2}(b_1 + b_2) \times h )
- Area of square, kite, and rhombus: ( \frac{1}{2}(d_1 \times d_2) )
Special Quadrilateral Properties
- In rhombuses and squares, diagonals bisect each other and are perpendicular bisectors.
- Trapezoids have one pair of opposite sides that are parallel, with legs as non-parallel sides.
Formulas Used in Quadrilaterals
- Distance formula proves congruence of opposite sides.
- Slope formula confirms parallel sides.
- Midpoint formula validates that diagonals bisect each other.
Additional Definitions
- Bases refer to the parallel sides in trapezoids and related shapes.
- Legs are the non-parallel sides of trapezoids.
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