Then: You determined whether quadrilaterals were parallelograms and/or rectangles. Now: 1. Recognize and apply the properties of rhombi and squares. 2.

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Then: You determined whether quadrilaterals were parallelograms and/or rectangles. Now: 1. Recognize and apply the properties of rhombi and squares. 2. Determine whether quadrilaterals are rectangles, rhombi, or squares. 6.5 RHOMBI AND SQUARES ges/rhombus/baseball-diamond-as-rhombus.gif

Parallelogram with all four sides congruent. *All the properties of a parallelogram RHOMBI

DIAGONALS OF A RHOMBUS

Theorem 6.16 If a parallelogram is a rhombus, then each diagonal bisect a pair of opposite angles. If ABCD is a rhombus, then  DCA   BCA   DAC   BAC DIAGONALS OF A RHOMBUS

The diagonals of rhombus WXYZ intersect at V. Use the given information to find each measure or value. a. If m  WZX = 39.5, find m  ZYX. b. If WX = 12 and VX = 5, find WV. c. If m  WZX = 41, find m  YWZ. EXAMPLE 1: USE PROPERTIES OF A RHOMBUS

d. If WX = 8x – 5 and WZ = 6x + 3, find x. e. If m  ZWY = 6y + 7 and m  XYW = 9y -5, find y. EXAMPLE 1:

Parallelograms with four congruent sides and four congruent angles. Parallelogram that is both a rectangle and a rhombus is a square. SQUARES

EFGH is a square. If GJ = 15, find each measure. a. m  EJF = b. m  JFG = c. FH = d. EJ = e. EF = SQUARES

CONCEPT SUMMARY: PARALLELOGRAMS

CONDITIONS FOR RHOMBI AND SQUARES

Theorem 6.18 If one diagonal of a parallelogram bisects a pair of opposite angles, then the parallelogram is a rhombus. If  1   2 and  3   4,or  5   6 and  7   8, then ABCD is a rhombus. CONDITIONS FOR RHOMBI AND SQUARES

Theorem 6.20 If a quadrilateral is both a rectangle and a rhombus, then it is a square. CONDITIONS FOR RHOMBI AND SQUARES SqRectRhom.jpg

GARDENING Hector is measuring the boundary of a new garden. He wants the garden to be square. He has set each of the corner stakes 6 feet apart. What does Hector need to know to make sure that the garden is square? EXAMPLE 2: USING PROPERTIES OF RHOMBI AND SQUARES

Determine whether parallelogram ABCD is a rhombus, a rectangle, or a square for A(–2, –1), B(–1, 3), C(3, 2), and D(2, –2). List all that apply. Explain. Step 1: The figure looks like _________________ EXAMPLE 4: CLASSIFY QUADRILATERALS USING COORDINATE GEOMETRY

Step 2: Are the diagonals congruent? Step 3: Are the diagonals perpendicular? EXAMPLE 4:

p #7-12 all, 14, evens, all, 44 Handout #14 – proof and #20 & 22 - graphs 6.5 ASSIGNMENT: