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Section 8.6 Identify Special Quadrilaterals

Section 8.6 Identify Special Quadrilaterals. Quadrilaterals. A polygon with four sides. Parallelograms. Kites. Trapezoids. A quadrilateral with both pairs of opposite sides parallel and congruent . A quadrilateral with 2 pairs of adjacent sides congruent and no opposite sides congruent. .

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Section 8.6 Identify Special Quadrilaterals

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  1. Section 8.6 Identify Special Quadrilaterals

  2. Quadrilaterals A polygon with four sides. Parallelograms Kites Trapezoids A quadrilateral with both pairs of opposite sides parallel and congruent. A quadrilateral with 2 pairs of adjacent sides congruent and no opposite sides congruent. A quadrilateral with exactly 1 pair of parallel sides. Rectangle Rhombus Isosceles Trapezoid Right Trapezoid A parallelogram with 4 congruent sides. A parallelogram with 4 right angles. A trapezoid whose 2 non-parallel sides are congruent. A trapezoid with exactly 2 right angles. Square A parallelogram with 4 congruent sides and 4 right angles.

  3. Parallelogram Theorems: • Thm. 8.3: If a quadrilateral is a parallelogram, then its opposite SIDES are • congruent. • Thm. 8.4: If a quadrilateral is a parallelogram, then its opposite ANGLES are • congruent. • Thm. 8. 5: If a quadrilateral is a parallelogram, then its consecutive angles are • SUPPLEMENTARY. • Thm. 8.6: If a quadrilateral is a parallelogram, then its diagonals bisect each • other. • Rhombus Theorems: • Thm. 8.11 A parallelogram is a rhombus if and only if its diagonals • are perpendicular. • Thm. 8.12 A parallelogram is a rhombus if and only if each diagonal • bisects a pair of opposite angles..

  4. Rectangle Theorems: • Thm. 8.13 A parallelogram is a rectangle if and only if its diagonals • are congruent. • REMEMBER:* The theorems that apply to parallelograms, ALSO apply to the special types of parallelograms – rhombus, rectangle and square.

  5. Kite Theorems: • Thm. 8.18 If a quadrilateral is a kite, then its diagonals • are perpendicular. • Thm. 8.19 If a quadrilateral is a kite, thenexactly one pair of • of opposite angles are congruent.

  6. REMEMBER: If it’s true for parallelograms, it’s true for ALL three types as well! Use the theorems and definitions of the quadrilaterals! X X X X X X X

  7. Right Trapezoid because it has one pair of || sides.

  8. Homework Section 8-6 Pg. 554 – 556 3 – 11, 14 – 16, 33 – 35, 43, 44, 47 – 50

  9. Geometry – Classifying Quadrilaterals Quadrilaterals Parallelograms Rhombus A polygon with four sides. Kites Trapezoids A quadrilateral with both pairs of opposite sides parallel and congruent. A quadrilateral with 2 pairs of adjacent sides congruent and no opposite sides congruent. A quadrilateral with exactly 1 pair of parallel sides. Rectangle Isosceles Trapezoid Right Trapezoid A parallelogram with 4 right angles. A parallelogram with 4 congruent sides. A trapezoid whose 2 non-parallel sides are congruent. A trapezoid with exactly 2 right angles. Square A parallelogram with 4 congruent sides and 4 right angles.

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