Warm-up #4 B A Can you say these are parallelograms? If yes, what theorem? __ ) (

Agenda Quiz Review Quiz Review Notes on Rectangles, Squares, Rhombuses Notes on Rectangles, Squares, Rhombuses Worksheet Worksheet HW – Workbook HW – Workbook Pg : 1-24

Table of Contents Rhombuses, Rectangles and Squares

6.4 Rhombuses, Rectangles and Squares Essential Question – What are the differences between rhombuses, rectangles, and squares?

Review of Parallelograms Properties Properties –Opposite sides  –Opposite sides –Opposite angles  –Consecutive angles supplementary supplementary –Diagonals bisect each other each other

Rectangles Properties Properties –All properties of parallelogram PLUS… –All four angles are congruent (all 90 o) AND…

A parallelogram is a rectangle if and only if its diagonals are congruent. A parallelogram is a rectangle if and only if its diagonals are congruent. DC BA  BD ABCD is a rectangle if and only if AC  BD

Rhombuses Properties Properties –All properties of a parallelogram PLUS… –All four sides congruent AND…

A parallelogram is a rhombus if and only if its diagonals are perpendicular. A parallelogram is a rhombus if and only if its diagonals are perpendicular.

Squares Properties Properties –All properties of a parallelogram –All properties of a rectangle –All properties of a rhombus | | | |

P ROPERTIES OF S PEC IAL P ARALLELOGRAMS parallelograms rhombusesrectangles squares

In the diagram, PQRS is a rhombus. What is the value of y? S OLUTION All four sides of a rhombus are congruent, so RS = PS. 5 y – 6 = 2 y + 3 Add 6 to each side. 5 y = 2 y + 9 Subtract 2y from each side. 3 y = 9 Divide each side by 3. y = 3 2y + 3 5y – 6 PQ RS Equate lengths of congruent sides.

If QR = 6, RS = 8, and <1 = 32 o, find the following: a. PS = b. PQ = c. QS = d. QT = e.<QPS = f. <2 = g. PT = h. <3 = i. <4 = S RQ P T PQRS is a Rectangle o 58 o 5 32 o

If AB = 8 and <ABC = 60 o, find the following: a. BC = b.<ABC = c.<1 = d.<2 = e.<3 = f.<4 = g. AE = h. EB = i. AC = 1 DC E 4 32 AB 60 o 8 30 o 4 8 4√3 ABCD is a Rhombus

If LM = 12, find the following: 1 3 P O M N L 4 2 LMNO is a Square a. MN = b.<LMN = c.<LPM = d.<1 = e.<3 = o 45 o

AAAA ssss ssss iiii gggg nnnn mmmm eeee nnnn tttt Workbook Pg : 1-24

AAAA ssss ssss eeee ssss ssss mmmm eeee nnnn tttt 321 Name 3 special types of parallelograms Name 2 special properties of rectangles Name 1 special property of squares