1. 6-2C Proofs with Special Parallelograms
What happens to the diagonals of parallelograms?
What happens to the diagonals of special parallelograms?

2. Use the terms parallelogram, rhombuses and rectangles to complete the statements.
All squares are ____
All rhombuses are ____
All rectangles are ____
Parallelograms, rectangles and rhombuses
Parallelograms

3. Parallelogram Draw a parallelogram on your paper.
Draw diagonals in your parallelogram.
Measure the diagonals. Are the diagonals congruent?
Do the diagonals bisect each other?
Diagonals of a parallelogram bisect each other.

4. Rhombus Draw a rhombus on your paper. Draw diagonals in your rhombus.
Measure the diagonals. Are the diagonals congruent?
Are the diagonals perpendicular?
A parallelogram is a rhombus if and only if its diagonals are perpendicular.

5. Rectangle Draw a rectangle on your paper.
Draw diagonals in your rectangle.
Measure the diagonals. Are the diagonals congruent?
Are the diagonals perpendicular?
A parallelogram is a rectangle if and only if its diagonals are congruent.

6. Square Draw a square on your paper. Draw diagonals in your square.
Measure the diagonals. Are the diagonals congruent?
Are the diagonals perpendicular?
A parallelogram is a square if and only if its diagonals are perpendicular and congruent.

7. Classify quadrilateral VWXY using the given information.
Parallelogram
b. Rhombus
c. Rectangle
d. Square

8. Find the value of x and y 2x −1= x + 2 x = 35 5
2x −1= x + 2
x = 3
x + 2 = 5
Diagonals bisect each other in a square.
2x − 1
x + 2
Use Pythagorean Theorem to find y.
= y2
= y2
50 = y2
square

9. If a parallelogram is a rectangle, then its diagonals are congruent.
Proof
Reasons
Given
All rect. are parallelogram
Def of rectangle
Def of rt triangle
Opp sides parallel congru
Reflexive
Leg-leg
CPCTC
Statements
DEFG is a rectangle
DEFG is a parallelogram
4. ∆DGF and ∆EFG are rt triangles

10. Theorems about Diagonals of Special Parallelograms
A parallelogram is a rhombus if and only if its diagonals are perpendicular.
A parallelogram is a rectangle if and only if its diagonals are congruent.
A parallelogram is a square if and only if its diagonals are both perpendicular and congruent.

11. What happens to the diagonals of parallelograms?
They bisect each other.
What happens to the diagonals of special parallelograms?
Rhombus—diagonals are perpendicular
Rectangle—diagonals are congruent.
Square—diagonals are perpendicular and congruent.

12. Assignment 6-2C
Page 430, 1-15
Copy the chart for 5-12