1. Chapter 5 Review

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

3. Sides - Paralleogram Opposite sides are congruent
Opposite sides are parallel

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

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

6. Definition
A rectangle is a quadrilateral with four right angles.

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

8. 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

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

10. Definition - Rhombus
A quadrilateral with four congruent sides.

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

12. 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

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

14. Square
Sides
All sides are congruent
Angles
All are right angles

15. 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

16. 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

17. 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

18. 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

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

20. 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

21. 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

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

23. 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

24. 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

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

26. 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.

27. 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