WARM-UP1. Find each variable.

x = 85° y = 39° z = 56°

2. Find each variable. a = 16 b = 8 c = 12 x = 70° y = 45° z = 25°

3. Given: ABCDEF is a regular hexagonProve: BCEF is a parallelogram

WARM-UPSTATEMENT REASONS

ABCDEF is a regular Hexagon Given

AB CD, AF DE, A D, BC FE Definition of a regular polygon

FAB EDC SAS

BF CE CPCTC

BCEF is a //-gram Both opp sides //-gram

STATEMENT REASONS

Rectangles (Section 6-4)

Thursday, April 20, 2023

Definition of a Rectangle

A quadrilateral with four right angles. A rectangle is a special type of parallelogram.

Theorems:

A parallelogram is a rectangle if and only if the diagonals are congruent.

Properties of Rectangles

Opposite sides are congruent and parallel. Opposite angles are congruent (90o). Consecutive angles are supplementary. Diagonals are congruent and bisect each

other. All four angles are right angles.

EXAMPLES:A woodworker constructs a rectangular picture frame so that JK = 50 cm and JL = 86 cm. Find HM.

EXAMPLES:A slab of concrete is poured with diagonal spacers. In rectangle CNRT, CN = 35 ft, and NT = 58 ft. Find each length.

1. TR

35 ft 29 ft2. CE

EXAMPLES:Quadrilateral RSTU is a rectangle. If RT = 6x + 4 and SU = 7x – 4, find x.

Answer: 8

EXAMPLES:Quadrilateral LMNP is a rectangle. Find x.

Answer: 10

EXAMPLES: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.

Answer: The perpendicular segments create four right angles. Therefore, by definition ABCD is a rectangle.

HOMEWORK: Page 344 #7-21 all, #25, 35, 46-47 (Due

Monday) Optional Quiz Review – Answers on online