Geometry Lesson 6 4 Rectangles Objective Recognize and

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 l Opposite angles are congruent (right) l Consecutive angles are supplementary l Diagonals bisect each other l NEW: Diagonals are congruent. l

Theorem Diagonals of a Rectangle l 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)2 32400 + (SR)2 = 40000 180 200 (SR)2 = 7600

If 64 64 26 26 26 64 64

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

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

Theorem 6. 14 l 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. 422 1 – 9 all, 10 – 18 E, 22 – 30 E, 50 – 60 E