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Section 8.6 Identify Special Quadrilaterals

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

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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..

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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.

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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, then exactly one pair of of opposite angles are congruent.

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

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

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

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Quadrilaterals KitesTrapezoids Rectangle Square Isosceles Trapezoid Right Trapezoid A polygon with four sides. 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. A parallelogram with 4 congruent sides. A parallelogram with 4 right angles. A trapezoid whose 2 non-parallel sides are congruent. A parallelogram with 4 congruent sides and 4 right angles. A trapezoid with exactly 2 right angles. Geometry – Classifying Quadrilaterals ParallelogramsParallelograms RhombusRhombus

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