1. All about parallelograms ….and trapezoids
May 20, 2008

2. Things to remember No headphone on during instruction.
No side conversations.
Be respectful and expect respect from others.
Don’t wander during instruction.

3. What is a parallelogram?
A parallelogram is a quadrilateral with both pairs of opposite sides parallel.

4. Properties of parallelograms
Opposite sides are parallel.
Opposite sides are congruent.
Opposite angles are congruent.
Diagonals bisect each other.
Total degrees of interior angles= 360

5. Five Ways to Prove a Quadrilateral is a Parallelogram
Show that both pairs of opposite sides are parallel.
Show that both pairs of opposite sides are congruent.
Show that one pair of opposite sides are both parallel and congruent.
Show that both pairs of opposite angles are congruent.
Show that the diagonals bisect each other.

6. What is a rectangle?
A rectangle is a parallelogram with four right angles.

7. What is a rhombus?
A rhombus is a parallelogram with four congruent sides.

8. What is a square?
A square is a parallelogram with four congruent sides and four right angles.

9. Comparison among figures

10. Finding values 3 3x

11. Practice proof Given: Parallelogram with diagonals AC and DB.
Prove: AC and DB bisect each other.

12. Another practice proof
Given: WZ is congruent to XY and WX is congruent to ZY. Prove: Quad. XYZW is a parallelogram

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

14. More about trapezoids
Notice that we can prove that exactly one pair of opposite sides of the quadrilateral above are parallel.
We have two lines cut by a transversal so that same side interior angles are supplementary.
The bases are the two parallel sides, not top and bottom.

15. Isosceles Trapezoids
A trapezoid with congruent legs is called an isosceles trapezoid.
If you cut out an isosceles trapezoid from a piece of paper and fold it over so that the legs coincide, you will find the both pair of base angles are congruent.

16. Theorem: The base angles of an isosceles trapezoid are congruent.
How would you show that angle A and angle B are congruent?

17. Diagonals of an isosceles trapezoid
What do you notice about the diagonals of the isosceles trapezoid?

18. Median of a Trapezoid
The median of a trapezoid is the segment that joins the midpoints of the legs.
The median of a trapezoid is very similar to the midsegment of a triangle in that both join the midpoints of sides.

19. Theorem: The median of a trapezoid
is parallel to the bases;
has a length equal to the average of the base lengths (i.e. 1/2 the sum of the lengths of the bases)

20. Using the median of trapezoid
What would you do to find x?

21. Finding angle measures in an isosceles trapezoid
Two congruent angles of an isosceles trapezoid have measures 3x + 10 and 5x -10. Find the value of x and then give the measures of all angles of the trapezoid.

22. Summary
In summary, a trapezoid is a special quadrilateral in which exactly one pair of opposite sides is parallel.
This, of course, means that a trapezoid is never a parallelogram since a parallelogram must have both pairs of opposite sides parallel.
An isosclele trapezoid is a trapezoid in which the legs are congruent ( which in turn means that the base angle and the diagonals are also congruent.).