WARM-UP 1) WXYZ is a rectangle. If ZX = 6x – 4 and WY = 4x + 14, find ZX. 2) WXYZ is a rectangle. If WY = 26 and WR = 3y + 4, find y. 3) RSTU is a rectangle.

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Presentation transcript:

WARM-UP 1) WXYZ is a rectangle. If ZX = 6x – 4 and WY = 4x + 14, find ZX. 2) WXYZ is a rectangle. If WY = 26 and WR = 3y + 4, find y. 3) RSTU is a rectangle. Find m  VRS. 4) RSTU is a rectangle. Find m  RVU.

6-5 R HOMBI AND S QUARES

R HOMBUS A quadrilateral with four congruent sides.

R HOMBUS The diagonals of a rhombus are perpendicular. Each diagonal of a rhombus bisects two angles.

ABCD IS A R HOMBUS Find the measure of angles 1, 2, 3, and 4. AB D C E º 1 4

E XAMPLE ALGEBRA The diagonals of rhombus WXYZ intersect at V. If WX = 8x – 5 and WZ = 6x + 3, find x. WX =WZ 8x – 5 = 6x + 3 2x – 5 =3 2x =8 x = 4

E XAMPLE m  CDB = 63 ABCD is a rhombus. Find m  CDB if m  ABC = 126. m  CDB is ½ of m  ABC

S QUARE A quadrilateral with four right angles and four congruent sides. It’s a combo of a rectangle and a rhombus!!!! ALL THEOREMS for a RECTANGLE and RHOMBUS also apply to a square.

V ENN D IAGRAM

E XAMPLE A.The diagonal bisects a pair of opposite angles. B.The diagonals bisect each other. C.The diagonals are perpendicular. D.The diagonals are congruent. Sachin has a shape he knows to be a parallelogram and all four sides are congruent. Which information does he need to know to determine whether it is also a square?

H OMEWORK Page 435 #7-12, 23-33, 50