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8.4 Rectangles

8.4 Rectangles. What you’ll learn: To recognize and apply properties of rectangles. To determine whether parallelograms are rectangles. Rectangles. Rectangle – a quadrilateral with 4 right angles. Theorem 8.13 If a parallelogram is a rectangle, then the diagonals are congruent.

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8.4 Rectangles

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  1. 8.4 Rectangles What you’ll learn: To recognize and apply properties of rectangles. To determine whether parallelograms are rectangles.

  2. Rectangles Rectangle – a quadrilateral with 4 right angles. Theorem 8.13 If a parallelogram is a rectangle, then the diagonals are congruent. Rectangles have all the properties of parallelograms plus 2 these 2.

  3. Properties of rectangles • Opposite sides parallel. • Opposite sides congruent. • Opposite angles are congruent. • Consecutive angles supplementary. • Diagonals bisect each other. • All four angles are right angles. • Diagonals are congruent.

  4. Theorem 8.14 If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.

  5. Quadrilateral RSTU is a rectangle. If RT=6x+4 and SU=7x-4, find x. If RS=x²+9 and TU=2x+44, find x. x²+9=2x+44 x²-2x-35=0 (x-7)(x+5)=0 x-7=0 x+5=0 x=7, -5 S T R U

  6. Determine whether ABCD is a rectangle. • A(-4,3), B(-2,4), C(1,-2), D(-1,-3) • A(0,5), B(4,7), C(5,4), D(1,2)

  7. Homeworkp. 42810-32 even,42, 52-62 even

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