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FINAL EXAM REVIEW

This review covers the key concepts and vocabulary related to parallelograms, rectangles, rhombuses, squares, and trapezoids. It includes the definition of a parallelogram, theorems about opposite sides, angles, and diagonals, as well as properties of rectangles and rhombuses. Also included are the definitions and theorems related to trapezoids and isosceles trapezoids. The review concludes with a homework assignment for Chapter 5.

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FINAL EXAM REVIEW

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  1. FINAL EXAM REVIEW Chapter 5 Key Concepts

  2. Chapter 5 Vocabulary parallelogram • opposite sides • opposite angles • diagonals rectangle rhombus square trapezoid

  3. Defn. of a Parallelogram A quadrilateral with both pairs of opposite sides parallel A B ABCD, In AB DC and AD BC D C

  4. Theorem Opposite sides of a parallelogram are congruent.

  5. Theorem Opposite angles of a parallelogram are congruent.

  6. Theorem Diagonals of a parallelogram bisect each other.

  7. Theorem ~ One pair of opp. sides both // and = Parallelogram

  8. The Five Ways to Show a Quadrilateral is a Parallelogram 1) Defn. of ~ 2) Both pairs of opp. sides = ~ 3) One pair of opp. sides both // and = ~ 7 4) Both pairs of opp. ‘s = 5) Diagonals bisect each other

  9. Theorem If 2 lines are parallel, then all points on one line are equidistant from the other line. A B AC = BD l m C D

  10. Theorem If 3 parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal. If AB = BC then XY = YZ A X B Y C Z

  11. Theorem A line that contains the midpoint of one side of a triangle and is parallel to another side passes through the midpoint of the third side. X If M is the midpoint of XY then N is the midpoint of XZ N M Y Z

  12. Theorem A segment that joins the midpoints of 2 sides of a triangle; 1. is parallel to the third side. 2. is half as long as the third side. X • MN YZ • MN = ½YZ N M Y Z

  13. Theorem: The diagonals of a rectangle are congruent

  14. Theorem: The diagonals of a rhombus are perpendicular.

  15. Theorem: Each diagonal of a rhombus bisects two angles of the rhombus.

  16. Theorem: The midpoint of the hypotenuse of a right triangle is equidistant from all three vertices. .

  17. Theorem: If an angle of a parallelogram is a right angle, then the parallelogram is a rectangle.

  18. Theorem: If two consecutive sides of a parallelogram are congruent, then the parallelogram is a rhombus.

  19. Trapezoid (Defn.) A quadrilateral with exactly one pair of parallel sides. leg base base leg

  20. IsoscelesTrapezoid (Defn.) A trapezoid with congruent legs.

  21. Theorem Base angles of an isosceles trapezoid are congruent.

  22. Theorem The median of a trapezoid: 1. is parallel to the bases. 2. has a length equal to the average of the base lengths. A B XY = ½(AB + CD) median X Y C D

  23. Homework • Chapter 5 Review WS

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