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WARM-UP

WARM-UP. Find each variable. x = 85 ° y = 39 ° z = 56 ° Find each variable. a = 16 b = 8 c = 12 x = 70 ° y = 45 ° z = 25 ° Given: ABCDEF is a regular hexagon Prove: BCEF is a parallelogram. WARM-UP. Rectangles (Section 6-4). Saturday, October 4, 2014.

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WARM-UP

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  1. WARM-UP • Find each variable. • x = 85° • y = 39° • z = 56° • Find each variable. • a = 16 • b = 8 • c = 12 • x = 70° • y = 45° • z = 25° • Given: ABCDEF is a regular hexagonProve: BCEF is a parallelogram

  2. WARM-UP

  3. Rectangles (Section 6-4) Saturday, October 4, 2014

  4. Definition of a Rectangle • A quadrilateral with four right angles. • A rectangle is a special type of parallelogram.

  5. Theorems: • A parallelogram is a rectangle if and only if the diagonals are congruent.

  6. 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.

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

  8. 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 2.CE 35 ft 29 ft

  9. EXAMPLES: Quadrilateral RSTU is a rectangle. If RT = 6x + 4 and SU = 7x – 4, find x. Answer: 8

  10. EXAMPLES: Quadrilateral LMNP is a rectangle. Find x. Answer: 10

  11. 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.

  12. HOMEWORK: • Page 344 #7-21 all, #25, 35, 46-47 (Due Monday) • Optional Quiz Review – Answers on online

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