Chapter 10 Introducing Geometry

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Chapter 10Introducing Geometry

• Section 10.5
• More About Quadrilaterals

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Quadrilateral

• A quadrilateral is a
• polygon with four sides.

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Trapezoid

• A trapezoid is a quadrilateral
• with exactly one pair of parallel sides.

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Isosceles Trapezoid

• An isosceles trapezoid is a trapezoid whose legs
  (non-parallel sides)
• are congruent.

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Properties of Isosceles Trapezoids

• Diagonals are congruent.
• Both pairs of base angles are congruent.

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Kite

• A kite is a quadrilateral
• with two distinct pairs of
• consecutive congruent sides.

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Properties of Kites

• Diagonals are perpendicular.
• One diagonal bisects one pair of opposite angles.

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Parallelogram

• A parallelogram is a
• quadrilateral with two pairs of parallel sides

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Properties of Parallelograms

• A quadrilateral is a parallelogram iff
• Opposite sides are parallel OR
• Opposite sides are congruent OR
• One pair of opposite sides are both
• congruent and parallel OR
• Opposite angles are congruent OR
• Consecutive angles are supplementary OR
• Diagonals bisect each other

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Rectangle

• A rectangle is a parallelogram
• with four right angles.

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Properties of Rectangles

• A parallelogram is a rectangle iff
• It has at least one right angle OR
• Its diagonals are congruent.

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Rhombus

• A rhombus is a parallelogram
• with four congruent sides.

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Properties of Rhombii

• A parallelogram is a rhombus iff
• It has four congruent sides OR
• Its diagonals bisect the angles OR
• Its diagonals are perpendicular
• bisectors of each other.

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Square

• A square is a parallelogram
• that has four right angles
• and four congruent sides.

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Properties of Squares

• A parallelogram is a square iff
• It is a rectangle with four congruent sides OR
• It is a rhombus with a right angle OR
• Its diagonals are congruent and
• perpendicular bisectors of each other.

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Quadrilateral Family Tree