Lesson 6-4 Rectangles. rectangle Recognize and apply properties of rectangles. Determine whether parallelograms are rectangles. Standard 7.0 Students.

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Presentation transcript:

Lesson 6-4 Rectangles

rectangle Recognize and apply properties of rectangles. Determine whether parallelograms are rectangles. Standard 7.0 Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles. (Key)

Rectangle Def—A //ogram with 4 Right Angles

Properties of a Rectangle Rectangle  Diagonals are  (Also has all the properties of a //ogram.) –Opposite sides  –Opposite angles  –Consecutive angles supplementary –Diagonals bisect each other

Given ABCD is a Rectangle, list everything that must be true. AB CD E #5: Diagonals bisect each other. #4: Consec.  s are Supp. #3: Opp.  s are  #2: Opp. Sides are  #1: Diagonals are  Def: 4 rt.  s //ogram: Opp. Sides //

Quadrilateral RSTU is a rectangle. If RT = 6x + 4 and SU = 7x – 4, find x. Diagonals of a Rectangle

Answer: 8 Diagonals of a Rectangle The diagonals of a rectangle are congruent, Definition of congruent segments Substitution Subtract 6x from each side. Add 4 to each side. Diagonals of a rectangle are .

A.A B.B C.C D.D A.x = –1 B.x = 3 C.x = 5 D.x = 10 Quadrilateral EFGH is a rectangle. If FH = 5x + 4 and GE = 7x – 6, find x.

Angles of a Rectangle Quadrilateral LMNP is a rectangle. Find x.

Angles of a Rectangle Answer: 10 Angle Addition Postulate Substitution Simplify. Subtract 10 from each side. Divide each side by 8.

1.A 2.B 3.C 4.D A.6 B.7 C.9 D.14 Quadrilateral EFGH is a rectangle. Find x.

Reminder Perpendicular lines have opposite reciprocal slopes. –Prove the sides of a quadrilateral are perpendicular and you have proven it is a rectangle.

Quadrilateral ABCD has vertices A(–2, 1), B(4, 3), C(5, 0), and D(–1, –2). Determine whether ABCD is a rectangle using the Slope Formula. Rectangle on a Coordinate Plane Method 1: Use the Slope Formula, to see if opposite sides are parallel and consecutive sides are perpendicular.

Rectangle on a Coordinate Plane = Slopes  // lines Opp. Reciprocal Slopes   lines //ogram with 4 right angles  Rectangle

Rectangle on a Coordinate Plane Method 2: Use the Distance Formula, to determine whether opposite sides are congruent.

Rectangle on a Coordinate Plane Opp. Sides   //ogram Find the length of the diagonals. //ogram w/  Diagonals  Rectangle

1.A 2.B 3.C A.yes B.no C.cannot be determined Quadrilateral WXYZ has vertices W(–2, 1), X(–1, 3), Y(3, 1), and Z(2, –1). Determine whether WXYZ is a rectangle using the Distance Formula.

A.A B.B C.C D.D Quadrilateral WXYZ has vertices W(–2, 1), X(–1, 3), Y(3, 1), and Z(2, –1). What are the lengths of diagonals WY and XZ? A. B.4 C.5 D.25

Homework pg 344:pg 344: 1, 2, 7, 8, 10, 13-21, 27-29