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Section 6.4 Rectangles

Section 6.4 Rectangles. Rectangle – a quadrilateral with four right angles. Since both pairs of opposite sides are congruent and parallel it is also a parallelogram. Properties: 1. opposite sides are congruent and parallel 2. Opposite angles are congruent

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Section 6.4 Rectangles

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  1. Section 6.4 Rectangles

  2. Rectangle – a quadrilateral with four right angles. • Since both pairs of opposite sides are congruent and parallel it is also a parallelogram. • Properties: • 1. opposite sides are congruent and parallel • 2. Opposite angles are congruent • 3. Consecutive angles are supplementary. • 4. Diagonals are congruent and bisect each other. • 5. All four angles are right angles.

  3. Ex. 1 Diagonals • Quadrilateral RSTU is a rectangle. If RT = 6x + 4 and SU = 7x – 4, find x. • Diagonals are congruent so • 6x + 4 = 7x – 4. • X = 8

  4. Ex. 2 Angles • Quadrilateral ABCD is a rectangle. Find y. • We know because parallel lines means alternate interior angles are congruent • Substitute • Set = 0 • Factor • Solve • Throw out y = -1 because that means angle = 0

  5. Ex. 3 Angle • Quadrilateral LMNP is a rectangle. Find x. • All angles are right angles • 5x + 8 + 3x + 2 = 90 • X = 10

  6. Ex. Coordinate plane

  7. P. 344 7 – 21, 24 – 29, 46, 47, 49 - 52

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