1. 1 Section 9: Rhombuses, Rectangles, and Squares

2. 2 Goals Use properties of diagonals of rhombuses, rectangles, and squares Use properties of sides and angles of rhombuses, rectangles, and squares Anchors Apply appropriate techniques, tools, and formulas to determine measurements. Analyze characteristics and properties of two and three dimensional geometric shapes and demonstrate understanding of geometric relationships.

3. 3 Properties of Special Parallelograms Rhombus All the properties of a parallelogram All four sides are congruent The diagonals are perpendicular The diagonals bisect the interior angles 90  x x x x y y y y

4. 4 All the properties of a parallelogram All sides meet at 90  Each of the diagonals are congruent Properties of Special Parallelograms Rectangle AB CD EAC = BD Makes two pairs of isosceles triangles. AE = EC = ED = EB xx xx y y y y

5. 5 Properties of Special Parallelograms Square All the properties of a parallelogram All the properties of a rhombus All the properties of a rectangle AB CD 45  90 

6. 6 Parallelogram RectanglesSquaresRhombuses

7. 7 Rectangle ABCD  ABE = 10x - 5  BCA = 4x – 3 Find all angles.  ABE +  BCA = 90  X = 7 25  65  130  50  10x - 5 + 4x - 3 = 90 

8. 8 Rectangle QRST  QRU = 4x + 4  RUQ = 15x - 12 Find all angles.  QRU +  RQU +  RUQ = 180  X = 8 4x + 4 + 4x + 4 + 15x - 12 = 180  36  54  108  72 

9. 9 Rhombus PROD  PRU = 9x - 4  PDU = 5x + 20 Find all angles.  PRU =  PDU 9x - 4 = 5x + 20 x = 6 90  50  40 

10. 10 Rhombus JELY  UEJ = 2x + 6  YLU = 4x Find all angles.  UEJ +  YLU = 90  x = 14 34  2x + 6 + 4x = 90  34  56  90 

11. 11 What special type of quadrilateral is ABCD? A ( -4, 7 ), B ( 6, 9 ), C ( 8, 16 ) D ( -2, 14 ) Slope of AB = Slope of BC = Slope of CD = Slope of AD = 1 / 5 7 / 2 1 / 5 7 / 2 Length of AB = Length of BC = Length of CD = Length of AD = 2√26 √53 2√26 √53 ABCD is a parallelogram – b/c it has two sets of parallel and congruent sides. How do we do that? What do we need to know?

12. 12 What special type of quadrilateral is EFGH? E ( 4, -8 ), F ( 7, -3 ), G ( 12, -6 ) H ( 9, -11 ) Slope of EF = Slope of FG = Slope of GH = Slope of EH = 5 / 3 -3 / 5 5 / 3 -3 / 5 Length of AB = Length of BC = Length of CD = Length of AD = √34 EFGH is a square – b/c it has two sets of parallel sides, all sides are congruent, and the slopes are negative reciprocals. How do we do that? What do we need to know?

13. 13 What special type of quadrilateral is IJKL? I ( -9, -9 ), J ( -6, -2 ), K ( -3, -9 ) L ( -6, -16 ) Slope of IJ = Slope of JK = Slope of KL = Slope of IL = 7 / 3 -7 / 3 7 / 3 -7 / 3 Length of IJ = Length of JK = Length of KL = Length of IL = √58 IJKL is a rhombus– b/c it has two sets of parallel sides and all sides are congruent, How do we do that? What do we need to know? Diagonals are perpendicular. Slope of IK = 0 and slope of JL is undefined.

14. 14 What special type of quadrilateral is MNOP? M ( 2, 2 ), N ( 5, 11 ), O ( 14, 14 ) P ( 11, 5 ) Slope of MN = Slope of NO = Slope of OP = Slope of MP = 3 1 / 3 3 1 / 3 Length of MN = Length of NO = Length of OP = Length of MP = 3√10 MNOP is a rhombus– b/c it has two sets of parallel sides and all sides are congruent, How do we do that? What do we need to know? Diagonals are perpendicular. Slope of MO = 1 and slope of NP = -1.