6-4 Properties of Special Parallelograms Geometry

Special Parallelograms Rhombus- a ||’ogram with 4 @ sides Rectangle- a ||’ogram with 4 rt s. Square- a ||’ogram with 4 @ sides and 4 rt s

So far: (we’ll add more later) _ Quadrilaterals _ parallelograms _ _ rhombus _ rectangle square

Corollaries Rhombus corollary- a quad is a rhombus iff it has 4 @ sides. Rectangle corollary- a quad is a rectangle iff it has 4 rt ‘s Square corollary- a quad is a square iff it is a rhombus and a rectangle.

Ex. 1 sometimes, always, never? A rhombus is a square. A parallelogram is a rectangle. A square is a regular quadrilateral. A rectangle is a quadrilateral. Sometimes Sometimes, if is has 4 rt ‘s Always

Properties of Rectangles 6-4-1 If a quadrilateral is a rectangle, then it is a parallelogram. B C ABCD is a parallelogram. A D

Properties of Rectangles Thm 6-4-2 A ||’ogram is a rectangle iff its diagonals are @. Q R If QRST is a rectangle then If then QRST is a rectangle. T S

Ex. 2 A woodworker constructs a rectangular picture frame so that JK = 50 cm & JL = 86 cm. Find HM. K L H J M ½ of 86 = 43 cm = HM

Properties of Rhombuses 6-4-3 If a quadrilateral is a rhombus, then it is a parallelogram. B C ABCD is a parallelogram A D

Properties of Rhombuses Thm 6-4-4 A parallelogram is a rhombus then its diagonals are . J K If , then JKLM is a rhombus. If JKLM is a rhombus, then __ __ M L

Properties of Rhombuses Thm 6-4-5 A ||ogram is a rhombus iff each diagonal bisects a pair of opposite s. B A (( ) (( ) )) )) ( ( D C

Ex. 3   A)TV= 7.9 B) 20°

Ex. 4 Show that diagonals of square EFGH are congruent perpendicular bisectors of each other. E(-4,-1), F(-1,3), G(3,0), H(0,-4). 1) graph 2) Show diagonals are congruent using distance formula for diagonals 3) Show slope of diagonals (which should be opposite & reciprocals of each other) 4) Show midpoint of both diagonals which should be the same order pair. Distance , slope & midpt formula

Graph for Ex. 4 1.) graph

2.) 3.) 4.)

Assignment