Geometry Lesson 6 – 4 Rectangles Objective: Recognize and apply properties of rectangles. Determine whether parallelograms are rectangles.

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Presentation transcript:

Geometry Lesson 6 – 4 Rectangles Objective: Recognize and apply properties of rectangles. Determine whether parallelograms are rectangles.

Rectangle A parallelogram with 4 right angles. Opposite sides are parallel and congruent Opposite angles are congruent (right) Consecutive angles are supplementary Diagonals bisect each other NEW: Diagonals are congruent.

Theorem Diagonals of a Rectangle If a parallelogram is a rectangle, then its diagonals are congruent.

A rectangular park has two walking paths as shown. If PS = 180 meters and PR = 200 meters, find QT and RS PR = QS QS = 200 QT = (1/2)(QS) QT = (1/2)(200) QT = 100 (PS) 2 + (SR) 2 = (PR) 2 (180) 2 + (SR) 2 = (200) (SR) 2 = (SR) 2 = 7600

If

Quadrilateral JKLM is a rectangle. If measure of angle KJL is 2x + 4 and measure of angle JLK is 7x + 5, find x. (2x + 4) o (7x + 5) o 2x x + 5 = 90 9x + 9 = 90 9x = 81 x = 9

Quadrilateral JKLM is a rectangle. If JP = 3y – 5 and MK = 5y + 1, find y. 3y - 5 5y + 1 2(JP) = MK 2(3y – 5) = 5y + 1 6y – 10 = 5y + 1 y = 11

Theorem Theorem 6.14 If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.

Quadrilateral PQRS has vertices P(-5, 3), R(-1, -4) Q(1, -1) and S (-7, 0). Determine whether PQRS is a rectangle by using the distance formula. First figure out if the quad is a parallelogram By doing one of the tests. Either prove opp sides are congruent or one set Of opp sides is parallel and congruent. Cont…

Figure out if the parallelogram is a rectangle: Diagonals of a rectangle are congruent. Quadrilateral PQRS is a rectangle.

Quadrilateral JKLM has vertices J(-10, 2) K(-8,-6) L(5, -3) M(2, 5) Determine whether JKLM is a rectangle using the Slope formula. To be a rectangle, consecutive sides must be perpendicular (opp. reciprocals) Since the slopes of consecutive sides are not opposite reciprocals the figure is not a rectangle.

Homework Pg – 9 all, 10 – 18 E, 22 – 30 E, 50 – 60 E