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Section 8.6Identify Special Quadrilaterals
Rhombus
Quadrilaterals
Parallelograms Kites Trapezoids
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.
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..
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.
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.
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
Right Trapezoid because it has one pair of || sides.
HomeworkSection 8-6Pg. 554 – 556
3 – 11, 14 – 16, 33 – 35,
43, 44, 47 – 50
Quadrilaterals
Kites Trapezoids
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
Parallelograms
Rhombus
