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Questions and Answers
What is a diagonal?
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?
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?
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?
What is a parallelogram?
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What is the property of parallelograms regarding opposite sides?
What is the property of parallelograms regarding opposite sides?
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What is the property of parallelograms regarding opposite angles?
What is the property of parallelograms regarding opposite angles?
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What is the relationship between consecutive angles in a parallelogram?
What is the relationship between consecutive angles in a parallelogram?
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What can be said about the right angles in a parallelogram?
What can be said about the right angles in a parallelogram?
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What is the property of the diagonals in a parallelogram?
What is the property of the diagonals in a parallelogram?
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What does it mean if each diagonal of a parallelogram separates it into two congruent triangles?
What does it mean if each diagonal of a parallelogram separates it into two congruent triangles?
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Under what condition is a quadrilateral a parallelogram based on opposite sides?
Under what condition is a quadrilateral a parallelogram based on opposite sides?
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Under what condition is a quadrilateral a parallelogram based on opposite angles?
Under what condition is a quadrilateral a parallelogram based on opposite angles?
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What condition determines if a quadrilateral is a parallelogram regarding diagonals?
What condition determines if a quadrilateral is a parallelogram regarding diagonals?
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What is the condition involving one pair of sides in a quadrilateral for it to be a parallelogram?
What is the condition involving one pair of sides in a quadrilateral for it to be a parallelogram?
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What is a rectangle?
What is a rectangle?
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What can be said about the diagonals of a rectangle?
What can be said about the diagonals of a rectangle?
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What does it imply if the diagonals of a parallelogram are congruent?
What does it imply if the diagonals of a parallelogram are congruent?
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What is a rhombus?
What is a rhombus?
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What is a square?
What is a square?
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What can be said about the diagonals of a rhombus?
What can be said about the diagonals of a rhombus?
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What does it mean if each diagonal of a rhombus bisects a pair of opposite angles?
What does it mean if each diagonal of a rhombus bisects a pair of opposite angles?
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What is the condition for a parallelogram to be a rhombus involving diagonals?
What is the condition for a parallelogram to be a rhombus involving diagonals?
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What condition determines if a parallelogram is a rhombus regarding angles?
What condition determines if a parallelogram is a rhombus regarding angles?
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What condition determines if a parallelogram is a rhombus regarding consecutive sides?
What condition determines if a parallelogram is a rhombus regarding consecutive sides?
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What does it imply if a quadrilateral is both a rectangle and a rhombus?
What does it imply if a quadrilateral is both a rectangle and a rhombus?
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What is a trapezoid?
What is a trapezoid?
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What are the bases of a trapezoid?
What are the bases of a trapezoid?
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What are the legs of a trapezoid?
What are the legs of a trapezoid?
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What is a base angle in a trapezoid?
What is a base angle in a trapezoid?
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What is an isosceles trapezoid?
What is an isosceles trapezoid?
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What is the mid segment of a trapezoid?
What is the mid segment of a trapezoid?
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What is a kite?
What is a kite?
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What can be said about the base angles in an isosceles trapezoid?
What can be said about the base angles in an isosceles trapezoid?
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What condition determines if a trapezoid is isosceles regarding bases?
What condition determines if a trapezoid is isosceles regarding bases?
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What is the condition for a trapezoid to be isosceles based on diagonals?
What is the condition for a trapezoid to be isosceles based on diagonals?
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What does the Trapezoid Midpoint Theorem state?
What does the Trapezoid Midpoint Theorem state?
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What can be said about the diagonals of a kite?
What can be said about the diagonals of a kite?
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What can be said about the angles in a kite?
What can be said about the angles in a kite?
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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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Description
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!