WARM-UP 1. 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 hexagon Prove: BCEF is a parallelogram
Jan 08, 2016
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