Lesson 8 4 Rectangles Lesson 6 3 Rectangles

Lesson 8 -4 Rectangles Lesson 6 -3: Rectangles 1

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. l l l Opposite sides are parallel. Opposite sides are congruent. Opposite angles are congruent. Consecutive angles are supplementary. Diagonals bisect each other. Lesson 6 -3: Rectangles 2

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

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

Examples……. 1) DE = x + 21 and EB = 3 x -15; Find DB 2) AC = 5 x + 8 and AE = 4 x + 1; Find EC A B 1 2 3 4 D E 5 6 Lesson 6 -3: Rectangles C 5

Examples……. 1) ے DAC = 7 x + 6 and ے BCA = x 2 – 2; Find x. 2) ے BDC = 3 x + 9 and ے ABD = x 2 – 1; Find ے ABD. A B 1 2 3 4 D E 5 6 Lesson 6 -3: Rectangles C 6