2. FINAL EXAM REVIEW Chapter 5 Key Concepts

3. Chapter 5 Vocabulary parallelogram ► opposite sides ► opposite angles ► diagonals rectanglerhombussquaretrapezoid

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

5. Theorem Opposite sides of a parallelogram are congruent.

6. Theorem Opposite angles of a parallelogram are congruent.

7. Theorem Diagonals of a parallelogram bisect each other.

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

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

10. Theorem If 2 lines are parallel, then all points on one line are equidistant from the other line. AB l m CD AC = BD

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

12. 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. YZ X M N If M is the midpoint of XY then N is the midpoint of XZ

13. 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. YZ X M N 1.MN YZ 2.MN = ½YZ

14. Theorem: The diagonals of a rectangle are congruent

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

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

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

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

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

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

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

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

23. Theorem The median of a trapezoid: 1. is parallel to the bases. 2. has a length equal to the average of the base lengths. median AB CD XY XY = ½(AB + CD)

24. Homework ► Chapter 5 Review WS