1. Vocabulary rectangle rhombus square Helpful Hint
Rectangles, rhombi, and squares are sometimes referred to as special parallelograms. They have all the properties of a parallelogram plus additional ones that identify them as a special parallelogram.
Helpful Hint

2. DEFINITIONS
A BICONDITIONAL STATEMENT WILL PROVIDE OF AND FOR PROPERTIES…

4. ADDITIONAL RHOMBI OF/FOR RULES

5. ADDITIONAL RECTANGLE OF/FOR RULES

6. RHOMBUS OF/FOR PROPERTIES
Properties OF Rhombus:
rhombus → 4  sides
rhombus →  diagonals
rhombus → diagonals bisect corner ’s
rhombus → llgram
Properties FOR Rhombus:
4  sides → rhombus
llgram with  diagonals → rhombus
llgram with diagonals bisect corner ’s → rhombus

7. RECTANGLE OF/FOR PROPERTIES
Properties OF Rectangle:
rectangle → 4 right ’s
rectangle →  diagonals
rectangle → llgram
Properties FOR Rectangle:
4 right ’s → rectangle
llgram with  diagonals → rectangle

8. Example 1a: Using Properties of Rhombuses to Find Measures
TVWX is a rhombus. Find TV and mVTZ.

9. Example 1b: Using Properties of Rhombuses to Find Measures
Given rhombus ABCD, find the angles:

10. Example 2: Verifying Properties of Squares
Show that the diagonals of square EFGH are congruent perpendicular bisectors of each other.

11. Check It Out! Example 3
The vertices of STVW are S(–5, –4), T(0, 2), V(6, –3) , and W(1, –9) . Find the most specific name for quadrilateral STVW.
Check if the diags bisect each other (llgram).
Check if the diags are congruent (rect).
Check if the diags are perpendicular (rhom).
Must be llgram to be rect or rhom, must be all 3 to be a square.

12. Example 4: Applying Conditions for Special Parallelograms
Determine if the conclusion is valid. If not, tell what additional information is needed to make it valid.
Given:
Conclusion: EFGH is a rhombus.
The conclusion is not valid. By Theorem 6-5-3, if one pair of consecutive sides of a parallelogram are congruent, then the parallelogram is a rhombus. By Theorem 6-5-4, if the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus. To apply either theorem, you must first know that ABCD is a parallelogram.

13. Check It Out! Example 4
Given: PQTS is a rhombus with diagonal
Prove:

14. Lesson Quiz: Part IV
6. Given: ABCD is a rhombus.
Prove: 

15. Lesson Quiz: Part III
1. Use the diagonals to determine whether a quadrilateral with vertices A(2, 7), B(7, 9), C(5, 4), and D(0, 2) is a llgram, rectangle, rhombus, or square. Give all the names that apply.
2. Given rectangle QRST,
find all angles:

16. Lesson Quiz: Part III
3. The vertices of ABCD are A(1, 3), B(3, 2), C(4, 4), and D(2, 5). Classify the quadrilateral.
4. Given: ABCD is a rhombus.
Prove:

17. WHO AM I?
Mark what you know as you go along…