Properties of Shapes Flashcards

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Questions and Answers

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)

  • 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)

  • 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)

<p>Diagonals are perpendicular. (B), All sides are congruent. (C), Diagonals bisect each other. (D)</p> Signup and view all the answers

What is a property of a trapezoid?

<p>Has exactly one pair of parallel sides. (B)</p> Signup and view all the answers

What is the area formula for a rectangle?

<p>l x w (A)</p> Signup and view all the answers

What is the area formula for a trapezoid?

<p>1/2(b1 + b2) x h</p> Signup and view all the answers

What does the distance formula prove about a parallelogram?

<p>Both pairs of opposite sides are congruent.</p> Signup and view all the answers

What does the slope formula prove about a parallelogram?

<p>Both pairs of opposite sides are parallel.</p> Signup and view all the answers

What does the midpoint formula prove in relation to diagonals?

<p>Diagonals bisect each other.</p> Signup and view all the answers

What is the formula for the area of a square?

<p>s^2 or 1/2(d1 x d2)</p> Signup and view all the answers

What is unique about the legs of a trapezoid?

<p>They are the non-parallel sides. (C)</p> Signup and view all the answers

What is a base in the context of a trapezoid?

<p>The name of parallel sides in a trapezoid.</p> Signup and view all the answers

Match the following shapes with their properties:

<p>Square = All four sides are congruent. Rectangle = All angles are right angles. Rhombus = Diagonals bisect each other. Trapezoid = Has exactly one pair of parallel sides.</p> Signup and view all the answers

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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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