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Chapter 8 Quadrilaterals
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Page 1: Chapter 8 Quadrilaterals. Section 8-1 Quadrilaterals.

Chapter 8Quadrilaterals

Page 2: Chapter 8 Quadrilaterals. Section 8-1 Quadrilaterals.

Section 8-1Quadrilaterals

Page 3: Chapter 8 Quadrilaterals. Section 8-1 Quadrilaterals.

Quadrilateral

A closed geometric figure with four sides and four vertices.

Page 4: Chapter 8 Quadrilaterals. Section 8-1 Quadrilaterals.

Any two sides, vertices, or angles of a quadrilateral are either consecutive or nonconsecutive.

Page 5: Chapter 8 Quadrilaterals. Section 8-1 Quadrilaterals.

Diagonals

Segments whose endpoints are nonconsecutive vertices of a quadrilateral

Page 6: Chapter 8 Quadrilaterals. Section 8-1 Quadrilaterals.

Theorem 8-1

The sum of the measures of the angles of a quadrilateral is 360°.

Page 7: Chapter 8 Quadrilaterals. Section 8-1 Quadrilaterals.

Section 8-2Parallelograms

Page 8: Chapter 8 Quadrilaterals. Section 8-1 Quadrilaterals.

Parallelogram

A quadrilateral with two pairs of parallel sides

Page 9: Chapter 8 Quadrilaterals. Section 8-1 Quadrilaterals.

Theorem 8-2

Opposite angles of a parallelogram are congruent.

Page 10: Chapter 8 Quadrilaterals. Section 8-1 Quadrilaterals.

Theorem 8-3

Opposite sides of a parallelogram are congruent.

Page 11: Chapter 8 Quadrilaterals. Section 8-1 Quadrilaterals.

Theorem 8-4

The consecutive angles of a parallelogram are supplementary.

Page 12: Chapter 8 Quadrilaterals. Section 8-1 Quadrilaterals.

Theorem 8-5

The diagonals of a parallelogram bisect each other.

Page 13: Chapter 8 Quadrilaterals. Section 8-1 Quadrilaterals.

Theorem 8-6

The diagonal of a parallelogram separates it into two congruent triangles.

Page 14: Chapter 8 Quadrilaterals. Section 8-1 Quadrilaterals.

Section 8-3Tests for Parallelograms

Page 15: Chapter 8 Quadrilaterals. Section 8-1 Quadrilaterals.

Theorem 8-7

If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Page 16: Chapter 8 Quadrilaterals. Section 8-1 Quadrilaterals.

Theorem 8-8

If one pair of opposite sides of a quadrilateral is parallel and congruent, then the quadrilateral is a parallelogram.

Page 17: Chapter 8 Quadrilaterals. Section 8-1 Quadrilaterals.

Theorem 8-9

If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

Page 18: Chapter 8 Quadrilaterals. Section 8-1 Quadrilaterals.

Section 8-4Rectangles, Rhombi, & Squares

Page 19: Chapter 8 Quadrilaterals. Section 8-1 Quadrilaterals.

Rectangle

A parallelogram with 4 right angles

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Rhombus

A parallelogram with 4 congruent sides

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Square

A parallelogram with 4 congruent sides and 4 right angles

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Theorem 8-10

The diagonals of a rectangle are congruent

Page 23: Chapter 8 Quadrilaterals. Section 8-1 Quadrilaterals.

Theorem 8-11

The diagonals of a rhombus are perpendicular

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Theorem 8-12

Each diagonal of a rhombus bisects a pair of opposite angles

Page 25: Chapter 8 Quadrilaterals. Section 8-1 Quadrilaterals.

Section 8-5Trapezoids

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Trapezoid

A quadrilateral with one pair of parallel sides

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Bases and Legs

The parallel sides are called bases

The nonparallel sides are called legs

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Base Angles

Each trapezoid has two pairs of base angles

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Median

The segment that joins the midpoints of its legs

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Theorem 8-13

The median of a trapezoid is parallel to the bases, and the length of the median equals one-half the sum of the lengths of the bases.

Page 31: Chapter 8 Quadrilaterals. Section 8-1 Quadrilaterals.

Theorem 8-14

Each pair of base angles in an isosceles trapezoid is congruent.