Standard G-4 Lesson 6-5 Objectives: 1. Review of lessons 6-1, 6-2 2. To determine whether a parallelogram is a rhombus or rectangle

Parallelograms Rectangles Rhombi Squares

› › › › › › Parallelograms Parallelograms are quadrilaterals with Both pairs of opposite sides parallel. ABCD › A B › › › › › D C

5 Things About Parallelograms Definition 1) Both Pairs Opp Sides Parallel Properties 2) Both Pairs Opp Sides Congruent 3) Both Pairs Opp Angles Congruent 4) Consecutive Angles Supplementary 5) Diagonals Bisect Each Other

Both Pairs Opp Sides Parallel AB||DC 1 and 6 3 and 8 AD||BC 2 and 5 4 and 7 1 3 2 4 7 5 8 6 D C Alternate Int Angles Are Congruent

Both Pairs Opp Sides Congruent 23 X = 23 2Y – 16 = 42 2Y = 58 Y = 29 42 2Y - 16 X

Both Pairs Opposite Angles Congruent X = 65 5Y – 5 = 115 5Y = 120 Y = 24 5Y - 5 X 115° 65°

Consecutive Angles Are Supplementary 1 3 2 4 Supplementary angles have a sum of 180

Diagonals Bisect Each Other BX = XD | || X AX = XC || | A D

Diagonals are congruent RECTANGLES Rectangles Are Parallelograms With 4 Right Angles All 5 Things About Parallelograms Are True…PLUS All angles = 90° Diagonals are congruent

All Angles = 90° If 1 Angle In A Parallelogram Is A Right Angle, Then All 4 Angles Are Right Angles This gives us right triangles also

Diagonals Are Congruent | This Gives Us 4 Congruent Segments And 4 Isosceles Triangles This Tells Us A Lot About The Angles

Congruent Pairs of Angles 2 3 1 4 11 9 10 12 8 5 7 6

Congruent Pairs of Angles 2 3 1 4 11 9 10 12 8 5 7 6

Diagonal are perpendicular Diagonals bisect opposite angles RHOMBI A Rhombus Is A Parallelogram With 4 Congruent Sides All 5 Things About Parallelograms Are True…PLUS 4 congruent sides Diagonal are perpendicular Diagonals bisect opposite angles

4 congruent sides 10 3Y + 1 = 10 3Y = 9 Y = 3 3Y + 1

Diagonal are perpendicular B 5 AB = The perimeter Of rhombus ABCD = XC = DB = 3 4 X 20 D C 3 8

The Square Is The Most Special Of All !! Everything That’s True For All The Others Is True For Squares.

QUADRILATERALS PARALLELOGRAMS RECTANGLES RHOMBI SQUARES

Theorem 1 If the diagonals of a parallelogram are perpendicular then it is a rhombus. If one diagonal of a parallelogram bisects the pair of opposite angles then the parallelogram is a rhombus. If the diagonals of a parallelogram are congruent then it is a rectangle.

Polygon Hierarchy Polygons Quadrilaterals Parallelograms Kites Trapezoids Isosceles Trapezoids Rectangles Rhombi Squares

Quadrilateral Characteristics Summary Convex Quadrilaterals 4 sided polygon 4 interior angles sum to 360 4 exterior angles sum to 360 Parallelograms Trapezoids Bases Parallel Legs are not Parallel Leg angles are supplementary Median is parallel to bases Median = ½ (base + base) Opposite sides parallel and congruent Opposite angles congruent Consecutive angles supplementary Diagonals bisect each other Rectangles Rhombi Isosceles Trapezoids All sides congruent Diagonals perpendicular Diagonals bisect opposite angles Angles all 90° Diagonals congruent Legs are congruent Base angle pairs congruent Diagonals are congruent Squares Diagonals divide into 4 congruent triangles

Objectives Recognize and apply the properties of rhombi All Parallelogram Properties All 4 Sides Congruent Diagonals bisect a pair of opposite ’s Diagonals form right angles with each other Recognize and apply the properties of squares All Rectangle Properties All Rhombus Properties Diagonals divide into 4 congruent ∆’s (45-45-90)

Vocabulary Rhombus – quadrilateral with all four sides congruent Square – a quadrilateral that is both a rhombus and a rectangle

Rhombi and Squares A Rhombus Characteristics All Parallelogram Properties All 4 Sides Congruent Diagonals bisect a pair of opposite ’s Diagonals form right angles with each other B C D A B Square Characteristics All Parallelogram Properties All Rectangle Properties All Rhombus Properties Diagonals divide into 4 congruent ∆’s C D

Kayla has a garden whose length and width are each 25 feet Kayla has a garden whose length and width are each 25 feet. If she places a fountain exactly in the center of the garden, how far is the center of the fountain from one of the corners of the garden? Answer: about 17.7 feet Example 5-4d

Textbook: page 348 Guided Practice: 1 thru 7 Practice/homework: 8 thru 13, 17 thru 22