Geometry: Polygons and Parallelograms
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Questions and Answers

What is the sum of the interior angles of a quadrilateral?

  • 720°
  • 360° (correct)
  • 540°
  • 180°

    • Which of the following describes a regular polygon?

  • All sides and angles are congruent (correct)
  • All angles are congruent
  • All sides are congruent
  • No sides are congruent

    • What is the measure of each exterior angle of a regular pentagon?

  • 90°
  • 108°
  • 60°
  • 72° (correct)

    • Which of the following properties is true for all parallelograms?

    <p>Opposite angles are congruent</p> Signup and view all the answers

    Which of the following statements about diagonals in a parallelogram is true?

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

    What is the formula to find the sum of the interior angles of a polygon with n sides?

    <p>$(n-2) imes 180°$</p> Signup and view all the answers

    Which of the following describes consecutive angles in a parallelogram?

    <p>They are supplementary</p> Signup and view all the answers

    What type of polygon is formed by connecting the midpoints of a quadrilateral's sides?

    <p>Parallelogram</p> Signup and view all the answers

    What distinguishes a rhombus from a rectangle?

    <p>A rhombus has perpendicular diagonals.</p> Signup and view all the answers

    Which statement is true about the diagonals of a rectangle?

    <p>They are congruent.</p> Signup and view all the answers

    Which of the following correctly characterizes a trapezoid?

    <p>It has exactly one pair of parallel sides.</p> Signup and view all the answers

    In an isosceles trapezoid, which property holds true?

    <p>Each pair of base angles are congruent.</p> Signup and view all the answers

    What is true regarding kites?

    <p>One pair of opposite angles is congruent.</p> Signup and view all the answers

    How is the midsegment of a trapezoid defined?

    <p>It is parallel to both bases.</p> Signup and view all the answers

    Which property is true about the angles in an isosceles trapezoid?

    <p>Only one pair of base angles are congruent.</p> Signup and view all the answers

    What is a characteristic of a square?

    <p>All sides and angles are congruent.</p> Signup and view all the answers

    Study Notes

    Polygons

    • A polygon is a closed figure consisting of straight segments.
    • A diagonal is a segment that joins nonconsecutive vertices of a polygon.
    • The sum of the interior angles of a polygon with n sides is (n-2)180°.
    • The sum of the angles of a triangle is 180°.
    • An equilateral polygon has all sides congruent.
    • An equiangular polygon has all angles congruent.
    • A regular polygon has all sides and all angles congruent.
    • The sum of the measures of exterior angles of a convex polygon is 360°.

    Parallelograms

    • A parallelogram is a quadrilateral with opposite sides parallel.
    • Opposite sides of a parallelogram are congruent.
    • Opposite angles of a parallelogram are congruent.
    • Consecutive angles in a parallelogram are supplementary.
    • The diagonals of a parallelogram bisect each other.

    Proving Parallelograms

    • If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
    • If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
    • If one pair of opposite sides of a quadrilateral are both parallel and congruent, then the quadrilateral is a parallelogram.
    • If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

    Special Parallelograms

    • A rhombus is a parallelogram with four congruent sides.
    • A rectangle is a parallelogram with four right angles.
    • A square is both a rhombus and a rectangle.
    • The diagonals of a rhombus are perpendicular bisectors to each other.
    • The diagonals of a rhombus bisect the opposite angles.
    • The diagonals of a rectangle are congruent.

    Trapezoids and Kites

    • A trapezoid is a quadrilateral with exactly one pair of parallel sides.
    • The parallel sides in a trapezoid are called the bases.
    • The non-parallel sides in a trapezoid are called the legs.
    • An isosceles trapezoid is a trapezoid with congruent legs.
    • Base angles of an isosceles trapezoid are congruent.
    • The diagonals of an isosceles trapezoid are congruent.
    • The midsegment of a trapezoid connects the midpoints of each leg. It is parallel to the bases and its length is the average of the lengths of the bases.
    • A kite is a quadrilateral with two pairs of consecutive congruent sides.
    • The diagonals of a kite are perpendicular.
    • One pair of opposite angles in a kite is congruent.

    Hierarchy of Quadrilaterals

    • All squares are rectangles.
    • All rectangles are parallelograms.
    • All rhombuses are parallelograms.
    • All parallelograms are quadrilaterals.
    • All kites are quadrilaterals.
    • All trapezoids are quadrilaterals.

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    Related Documents

    Geometry-07-Quadrilaterals-and-Other-Polygons PDF

    Description

    Test your knowledge of polygons and parallelograms in this quiz. Explore key properties, angle sums, and definitions surrounding these geometric shapes. Perfect for students looking to reinforce their understanding of geometry fundamentals.

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