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RECTANGLES

RECTANGLES. Recognize and apply properties of rectangles. Determine whether parallelograms are rectangles. Parts of the tennis court are marked by parallel and perpendicular lines. PROPERTIES OF RECTANGLES. A rectangle is a quadrilateral with four right angles.

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RECTANGLES

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  1. RECTANGLES • Recognize and apply properties of rectangles. • Determine whether parallelograms are rectangles. Parts of the tennis court are marked by parallel and perpendicular lines.

  2. PROPERTIES OF RECTANGLES A rectangle is a quadrilateral with four right angles. Since both pairs of opposite angles are congruent, it follows that a rectangle is a special type of parallelogram.

  3. THEOREM DIAGONALS OF A RECTANGLE If a parallelogram is a rectangle, then the diagonals are congruent. A B D C

  4. Key ConceptRectangles Properties A B Opposite sides are congruent and parallel D C

  5. Key ConceptRectangles Properties A B Opposite sides are congruent and parallel Opposite angles are congruent D C

  6. Key ConceptRectangles Properties A B Opposite sides are congruent and parallel Opposite angles are congruent Consecutive angles are supplementary D C

  7. Key ConceptRectangles Properties A B Opposite sides are congruent and parallel Opposite angles are congruent Consecutive angles are supplementary Diagonals are congruent and bisect each other. D C

  8. Key ConceptRectangles Properties A B Opposite sides are congruent and parallel Opposite angles are congruent Consecutive angles are supplementary Diagonals are congruent and bisect each other. All four angles are right angles. D C

  9. Example 1Diagonals of a Rectangle P O MNOP is a rectangle MO is 6x + 14, PN is 9x + 5 Find x M N

  10. Example 1Diagonals of a Rectangle P O MNOP is a rectangle MO is 6x + 14, PN is 9x + 5 Find x M N Solution: Diagonals of a rectangle are congruent Subtract 6x from each side Subtract 5 from each side Divide each side by 3

  11. Example 2Angles of a Rectangle (4x + 5)° A D Find x (9x + 20)° B C

  12. Example 2Angles of a Rectangle (4x + 5)° A D Find x (9x + 20)° B C Solution: Angle addition theorem Simplify Subtract 25 from each side Divide each side by 13

  13. PROVE THAT PARALLELOGRAMS ARE RECTANGLES THEOREM If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle A B D C

  14. Example 3Rectangle on a Coordinate Plane Quadrilateral F(-4, -1), G(-2, -5), H(4, -2), J(2, 2) Determine whether FGHI is a rectangle. J 2 1 -4 -2 2 4 F -1 H -2 -3 -4 -5 G

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