Lesson 6-3 Rectangles Lesson 6-3: Rectangles

Rectangles Definition: A rectangle is a parallelogram with four right angles. A rectangle is a special type of parallelogram. Thus a rectangle has all the properties of a parallelogram. Opposite sides are parallel. Opposite sides are congruent. Opposite angles are congruent. Consecutive angles are supplementary. Diagonals bisect each other. Lesson 6-3: Rectangles

Properties of Rectangles Theorem: If a parallelogram is a rectangle, then its diagonals are congruent. Therefore, ∆AEB, ∆BEC, ∆CED, and ∆AED are isosceles triangles. E D C B A Converse: If the diagonals of a parallelogram are congruent , then the parallelogram is a rectangle. Lesson 6-3: Rectangles

Examples……. If AE = 3x +2 and BE = 29, find the value of x. If AC = 21, then BE = _______. If m<1 = 4x and m<4 = 2x, find the value of x. If m<2 = 40, find m<1, m<3, m<4, m<5 and m<6. x = 9 units 10.5 units x = 18 units 6 5 4 3 2 1 E D C B A m<1=50, m<3=40, m<4=80, m<5=100, m<6=40 Lesson 6-3: Rectangles