FINAL EXAM REVIEW Chapter 5 Key Concepts
Chapter 5 Vocabulary parallelogram • opposite sides • opposite angles • diagonals rectangle rhombus square trapezoid
Defn. of a Parallelogram A quadrilateral with both pairs of opposite sides parallel A B ABCD, In AB DC and AD BC D C
Theorem Opposite sides of a parallelogram are congruent.
Theorem Opposite angles of a parallelogram are congruent.
Theorem Diagonals of a parallelogram bisect each other.
Theorem ~ One pair of opp. sides both // and = Parallelogram
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
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
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
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
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
Theorem: The midpoint of the hypotenuse of a right triangle is equidistant from all three vertices. .
Theorem: If an angle of a parallelogram is a right angle, then the parallelogram is a rectangle.
Theorem: If two consecutive sides of a parallelogram are congruent, then the parallelogram is a rhombus.
Trapezoid (Defn.) A quadrilateral with exactly one pair of parallel sides. leg base base leg
IsoscelesTrapezoid (Defn.) A trapezoid with congruent legs.
Theorem Base angles of an isosceles trapezoid are congruent.
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
Homework • Chapter 5 Review WS