Glencoe Geometry Chapter 6
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Glencoe Geometry Chapter 6

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Questions and Answers

What is a diagonal?

In a polygon, a segment that connects nonconsecutive vertices of the polygon.

What does the Polygon Interior Angle Sum Theorem state?

The sum of the interior angle measures of an n-sided convex polygon is (n-2)*180.

What does the Polygon Exterior Angles Sum Theorem state?

The sum of the exterior angle measures of a convex polygon, one angle at each vertex, is 360.

What is a parallelogram?

<p>A quadrilateral with parallel opposite sides.</p> Signup and view all the answers

What is the property of parallelograms regarding opposite sides?

<p>If a quadrilateral is a parallelogram, then its opposite sides are congruent.</p> Signup and view all the answers

What is the property of parallelograms regarding opposite angles?

<p>If a quadrilateral is a parallelogram, then its opposite angles are congruent.</p> Signup and view all the answers

What is the relationship between consecutive angles in a parallelogram?

<p>If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.</p> Signup and view all the answers

What can be said about the right angles in a parallelogram?

<p>If a parallelogram has one right angle, then it has four right angles.</p> Signup and view all the answers

What is the property of the diagonals in a parallelogram?

<p>If a quadrilateral is a parallelogram, then its diagonals bisect each other.</p> Signup and view all the answers

What does it mean if each diagonal of a parallelogram separates it into two congruent triangles?

<p>If a quadrilateral is a parallelogram, then each diagonal separates the parallelogram into two congruent triangles.</p> Signup and view all the answers

Under what condition is a quadrilateral a parallelogram based on opposite sides?

<p>If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.</p> Signup and view all the answers

Under what condition is a quadrilateral a parallelogram based on opposite angles?

<p>If both pairs of opposite angles are congruent, then the quadrilateral is a parallelogram.</p> Signup and view all the answers

What condition determines if a quadrilateral is a parallelogram regarding diagonals?

<p>If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.</p> Signup and view all the answers

What is the condition involving one pair of sides in a quadrilateral for it to be a parallelogram?

<p>If one pair of opposite sides of a quadrilateral is both parallel and congruent, then the quadrilateral is a parallelogram.</p> Signup and view all the answers

What is a rectangle?

<p>A quadrilateral with four right angles.</p> Signup and view all the answers

What can be said about the diagonals of a rectangle?

<p>If a parallelogram is a rectangle, then its diagonals are congruent.</p> Signup and view all the answers

What does it imply if the diagonals of a parallelogram are congruent?

<p>If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.</p> Signup and view all the answers

What is a rhombus?

<p>A quadrilateral with all 4 sides congruent.</p> Signup and view all the answers

What is a square?

<p>A quadrilateral with 4 right angles and 4 congruent sides.</p> Signup and view all the answers

What can be said about the diagonals of a rhombus?

<p>If a parallelogram is a rhombus, then its diagonals are perpendicular.</p> Signup and view all the answers

What does it mean if each diagonal of a rhombus bisects a pair of opposite angles?

<p>If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles.</p> Signup and view all the answers

What is the condition for a parallelogram to be a rhombus involving diagonals?

<p>If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.</p> Signup and view all the answers

What condition determines if a parallelogram is a rhombus regarding angles?

<p>If one diagonal of a parallelogram bisects a pair of opposite angles, then the parallelogram is a rhombus.</p> Signup and view all the answers

What condition determines if a parallelogram is a rhombus regarding consecutive sides?

<p>If one pair of consecutive sides of a parallelogram are congruent, then the parallelogram is a rhombus.</p> Signup and view all the answers

What does it imply if a quadrilateral is both a rectangle and a rhombus?

<p>If a quadrilateral is both a rectangle and a rhombus, then it is a square.</p> Signup and view all the answers

What is a trapezoid?

<p>A quadrilateral with exactly one pair of parallel sides.</p> Signup and view all the answers

What are the bases of a trapezoid?

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

What are the legs of a trapezoid?

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

What is a base angle in a trapezoid?

<p>Formed by the base and one of the legs.</p> Signup and view all the answers

What is an isosceles trapezoid?

<p>The legs of a trapezoid are congruent.</p> Signup and view all the answers

What is the mid segment of a trapezoid?

<p>The segment that connects the midpoints of the legs of the trapezoid.</p> Signup and view all the answers

What is a kite?

<p>A quadrilateral with exactly two pairs of adjacent congruent sides.</p> Signup and view all the answers

What can be said about the base angles in an isosceles trapezoid?

<p>If a trapezoid is isosceles, then each pair of base angles is congruent.</p> Signup and view all the answers

What condition determines if a trapezoid is isosceles regarding bases?

<p>If a trapezoid has one pair of congruent bases, then it is an isosceles trapezoid.</p> Signup and view all the answers

What is the condition for a trapezoid to be isosceles based on diagonals?

<p>A trapezoid is isosceles if and only if its diagonals are congruent.</p> Signup and view all the answers

What does the Trapezoid Midpoint Theorem state?

<p>The mid segment of a trapezoid is parallel to each base and its measure is one half the sum of the lengths of the bases.</p> Signup and view all the answers

What can be said about the diagonals of a kite?

<p>If a quadrilateral is a kite, then its diagonals are perpendicular.</p> Signup and view all the answers

What can be said about the angles in a kite?

<p>If a quadrilateral is a kite, then exactly one pair of opposite angles is congruent.</p> Signup and view all the answers

Study Notes

Diagonal

  • A diagonal connects nonconsecutive vertices in a polygon.

Polygon Interior Angle Sum Theorem 6.1

  • For an n-sided convex polygon, the sum of interior angles is calculated as (n-2)×180 degrees.

Polygon Exterior Angles Sum Theorem 6.2

  • The sum of the exterior angles of a convex polygon, one angle at each vertex, equals 360 degrees.

Parallelogram

  • A quadrilateral with parallel opposite sides; any side may serve as the base.

Properties of Parallelograms 6.3

  • Opposite sides of a parallelogram are congruent.

Properties of Parallelograms 6.4

  • Opposite angles of a parallelogram are congruent.

Properties of Parallelograms 6.5

  • Consecutive angles of a parallelogram are supplementary.

Properties of Parallelograms 6.6

  • If one angle of a parallelogram is a right angle, all angles are right angles.

Properties of Parallelograms 6.7

  • Diagonals of a parallelogram bisect each other.

Properties of Parallelograms 6.8

  • Each diagonal of a parallelogram separates it into two congruent triangles.

Conditions for Parallelograms 6.9

  • A quadrilateral is a parallelogram if both pairs of opposite sides are congruent.

Conditions for Parallelograms 6.10

  • A quadrilateral is a parallelogram if both pairs of opposite angles are congruent.

Conditions for Parallelograms 6.11

  • A quadrilateral is a parallelogram if its diagonals bisect each other.

Conditions for Parallelograms 6.12

  • A quadrilateral is a parallelogram if one pair of opposite sides is both parallel and congruent.

Rectangle

  • A quadrilateral with four right angles.

Diagonals in a Rectangle 6.13

  • In rectangles, diagonals are congruent.

Diagonals in a Rectangle 6.14

  • If diagonals of a parallelogram are congruent, it is a rectangle.

Rhombus

  • A quadrilateral with all sides congruent.

Square

  • A quadrilateral with four right angles and four congruent sides.

Diagonals of a Rhombus 6.15

  • Diagonals of a rhombus are perpendicular to each other.

Diagonals of a Rhombus 6.16

  • Each diagonal of a rhombus bisects a pair of opposite angles.

Conditions for Rhombi and Squares 6.17

  • A parallelogram with perpendicular diagonals is a rhombus.

Conditions for Rhombi and Squares 6.18

  • If a diagonal of a parallelogram bisects a pair of opposite angles, it is a rhombus.

Conditions for Rhombi and Squares 6.19

  • A parallelogram is a rhombus if one pair of consecutive sides is congruent.

Conditions for Rhombi and Squares 6.20

  • A quadrilateral that is both a rectangle and a rhombus is a square.

Trapezoid

  • A quadrilateral with exactly one pair of parallel sides.

Bases

  • The parallel sides of a trapezoid are called the bases.

Legs of a Trapezoid

  • The nonparallel sides of a trapezoid are known as the legs.

Base Angle

  • Formed by a base and one of the legs in a trapezoid.

Isosceles Trapezoid

  • A trapezoid where the legs are congruent.

Mid Segment of a Trapezoid

  • Connects the midpoints of the legs; parallel to the bases.

Kite

  • A quadrilateral with two pairs of adjacent congruent sides.

Isosceles Trapezoid 6.21

  • In an isosceles trapezoid, each pair of base angles is congruent.

Isosceles Trapezoid 6.22

  • A trapezoid with one pair of congruent bases is isosceles.

Isosceles Trapezoid 6.23

  • A trapezoid is isosceles if and only if its diagonals are congruent.

Trapezoid Midsegment Theorem 6.24

  • The midsegment is parallel to the bases and measures half the sum of the lengths of the bases.

Kites 6.25

  • The diagonals of a kite are perpendicular.

Kites 6.26

  • In a kite, exactly one pair of opposite angles is congruent.

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Explore the key concepts of Chapter 6 in Glencoe Geometry with essential flashcards. This chapter focuses on understanding diagonals, the interior angle sum theorem, and the exterior angle sum theorem for polygons. Perfect for reinforcing your geometry knowledge and preparing for exams!

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