Chapter 5 Review

Definition A parallelogram is a quadrilateral with both pairs of opposite sides parallel. NOTATION A B D C ABCD

Sides - Paralleogram Opposite sides are congruent Opposite sides are parallel

Theorem Opposite angles of a parallelogram are congruent Consecutive angles are supplementary A B D C 103 77 77 103

Diagonals of a parallelogram bisect each other. Theorem Diagonals of a parallelogram bisect each other. A B D C

Definition A rectangle is a quadrilateral with four right angles.

Rectangle Sides Angles Opposite sides are congruent Opposite sides are parallel Angles Four right angles

Recall that a rectangle is a parallelogram Recall that a rectangle is a parallelogram. Therefore a rectangle has all the same properties that a Parallelogram has! A rectangle also has some unique properties. A Rectangle: The diagonals bisect each other Unique Properties The diagonals are congruent

The diagonals of a rectangle are congruent. Rectangle Properties The diagonals of a rectangle are congruent. R E T C RC = ET

Definition - Rhombus A quadrilateral with four congruent sides.

Rhombus Sides Angles All sides are congruent Opposite angles are congruent Consecutive angles are supplementary

Recall that a rhombus is a parallelogram Recall that a rhombus is a parallelogram. Therefore a rhombus has all the same properties that a Parallelogram has! A rhombus also has some unique properties. A Rhombus: The diagonals bisect each other Unique Properties The diagonals are perpendicular Each diagonal of a rhombus bisects two angles of the rhombus

Definition - Square A quadrilateral with four right angles and four congruent sides.

Square Sides All sides are congruent Angles All are right angles

A Square can also be defined as a……….. Parallelogram Rectangle Rhombus A Square: The diagonals bisect each other The diagonals are congruent The diagonals are perpendicular Each diagonal of a square bisects two angles of the square

Definition A trapezoid is a quadrilateral with exactly one pair of parallel sides. The parallel sides are called the bases The other sides are called the legs

Definition An isosceles trapezoid is a trapezoid with congruent legs. THEOREM: Base angles of an isosceles trapezoid are congruent BASE A D If trapezoid ABCD has AB = DC, then <A = <D and <B = <C B C BASE

Theorem If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram 10 A B D C 7 7 10

Theorem If both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram A B D C

Theorem If one pair of opposite sides of a quadrilateral are both congruent and parallel, then the quadrilateral is a parallelogram. 10 A B D C 10

Theorem If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram A B D C 103 77 77 103

Theorem If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. A B D C

THEOREM The midpoint of the hypotenuse of a right triangle is equidistant from the three vertices. A C B X If ABC has right <ABC and X is the midpoint of AC, then 5 5 5 BX = AX = XC

THEOREM The median of a trapezoid is parallel to the bases and has a length equal to the average of the base lengths. Median = (6+10)/2 6 cm Median = 16/2 8 cm Median = 8 cm 10 cm

THEOREM If three parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal

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.

Theorem The segment that joins the midpoints of two sides of a triangle is half as long as the third side. N A C E D 5 10