1. Agenda 1) Bell Work 2) Outcomes 3) Investigation with Rhombi
4) Special Parallelogram properties
5) Finding pieces of special parallelograms
6) Discuss Thursday/Friday quiz

2. Bell Work 3/12/13
1) Can you prove that the following is a parallelogram? If so, state why/why not.
a) b)
2) Find the measure of the variables(b and c are parallelograms)
a) b) c)

3. 3/12/13 Outcomes I will be able to:
1) Determine if a parallelogram is a rectangle, rhombus or square
2) Find missing angles and side lengths of rectangles, rhombi and squares

4. Paper and Rhombi
On the back of your bell work, draw two sets of parallel lines by tracing the top and the bottom of your straight edge.
Your drawing should look like this:
Label the vertices:
A, B, C, D
Measure AB, BC, CD, and AD
What do you notice? A B D C

5. Rhombus The figure we just created was a Rhombus
So, a Rhombus is a parallelogram with…
All sides congruent
Draw in the diagonals and label the point in the middle E.
Look at the angles in the middle, what are they?
90°
So the diagonals
are perpendicular A B E D C

6. Rectangle Now draw a rectangle. ***Be sure to draw in the diagonals
Measure the diagonals. What do you notice?
They are congruent

7. Special Parallelogram Notes
all sides congruent
all angles congruent
all sides are congruent and
all angles are congruent
***So, a square is both a rhombus and a rectangle

8. Special Parallelogram Notes

9. Special Parallelogram Notes
sometimes
always
sometimes
sometimes
always

10. Special Parallelogram Notes
Example 3: EFGH is a rectangle. K is the midpoint of FH. If EG = 8x – 16, what are EK and GK? E F
If K is the midpoint of FH,
then we know that it is
also the midpoint of EG. K H G
How do we solve for EK and GK?
EK = 4x – 8
GK = 4x - 8

11. Special Parallelogram Notes
It has
four congruent sides
it has
four congruent angles
it has four congruent
sides and four congruent angles(it is a rhombus and a rectangle)

12. Examples What do we know about the sides of a rhombus?
They are equal: So: 2x = 3x - 16
x = 16

13. Examples What do we have to solve for first?
What do we know about the angles of a
square?
They equal 90°. So: 8x = 90
x = 10
What do we know about the sides of a square?
They are equal. So: 2y = x Substituting 10 in for x. 2y = 14
y = 7

14. Special Parallelogram Notes
rhombus
perpendicular

15. Special Parallelograms
rhombus
bisects

16. Special Parallelogram Notes
rectangle
diagonals
Meaning: AC is congruent to BD.

17. Examples
Rectangle
Yes, because if the diagonals intersect at a 90° angle that
means the shape is rhombus. If the shape is both a
rhombus and a rectangle, then it is a square.
Mr McGrew ur the man

18. Quiz Items Special Right Triangles
Using Trig ratios to find missing side lengths in right triangles
Using Trig ratios to find missing angles in right triangles
Classifying polygons(Convex/Concave, and by name: pentagon, hexagon, etc.)
Finding angle measures in quadrilaterals
Properties of parallelograms