Chapter 6 Quadrilaterals
6-1 Objectives _______________________________________________________ _______________________________________________________
Polygon Angle-Sum Theorem The sum of the measures of the interior angles of an n-gon is ____________________, where n is the _______________________ What is the sum of the interior angle measures of a hexagon? What is the sum of the interior angle measures of a 17-gon?
Corollary to the Polygon Angle-Sum Theorem Regular Polygon: a polygon that is both ___________________ and _________________ Corollary to the Polygon Angle-Sum Theorem: the measure of each interior angle of a regular n-gon is __________________________ What is the measure of an interior angle of a regular octagon?
Find the value of the variable
Practice: p. 356 #7, 8, 15-19 Complete on separate sheet of paper to turn in!
6-2 Objectives _______________________________________________________ _______________________________________________________
Parallelograms A parallelogram is a _____________________ with both pairs of opposite sides __________________. Opposite sides: do not share a _______________ Opposite angles: do not share a ______________ Consecutive angles: angles of a polygon that share a _____________
Properties of Parallelograms If a quadrilateral is a parallelogram, then its opposite sides are ___________________. If a quadrilateral is a parallelogram, then its consecutive angles are ___________________. If a quadrilateral is a parallelogram, then its opposite angles are ___________________. If quadrilateral is a parallelogram, then its diagonals _________________________________.
Using properties of parallelograms Find the length of: TU= VT=
Using properties of parallelograms Find the value of x. Find the value of y. Find mEDG. Find EH.
Practice: p. 364 #14, 15, 25-27, 29, 30, 38-40 Complete on separate sheet of paper to turn in!
6-4 Objectives _______________________________________________________ _______________________________________________________
Definition of rhombuses, rectangles, and squares Rhombus: a parallelogram with four ________________________. Rectangle: a parallelogram with four ________________________. Square: a parallelogram with four __________________________ and four _____________________________.
Properties of a rhombus If a parallelogram is a rhombus, then its diagonals are __________________. If a parallelogram is a rhombus, then each diagonal ______________ a pair of opposite angles.
Properties of a rectangle If a parallelogram is a rectangle, then its diagonals are ____________.
Practice: p. 380 #15-19, 24-27, 42-44, 45 Complete on separate sheet of paper to turn in!
6-6 Objective _______________________________________________________ _______________________________________________________
Definitions and properties of trapezoids and kites If a quadrilateral is a trapezoid, then it has exactly one pair of __________________________. If a quadrilateral is an isosceles trapezoid, then each pair of base angles is ____________________. If a quadrilateral is an isosceles trapezoid, then its diagonals are ____________________. If a quadrilateral is a kite, then it has 2 pairs of consecutive sides ___________________ and no opposite sides congruent. If a quadrilateral is a kite, then its diagonals are _______________________.
Find the values of x and y.
Find the values of the missing angles of each kite.
Practice: p. 395 #28-30, 34-36 Complete on separate sheet of paper to turn in!