1. Section 6.4 rhombuses, rectangles and squares
OBJECTIVES:
To define and classify special types of parallelograms
To use properties of diagonals of rhombuses and rectangles
BIG IDEA: Reasoning and Proof
ESSENTIAL UNDERSTANDING
The special parallelograms, rhombus, rectangle, and square, have basic properties about their sides, angles and diagonals that help identify them.
MATHEMATICAL PRACTICE: Make sense of problems and persevere in solving them.

2. Special types of Parallelograms
Rhombus: a parallelogram with ____________ _______________ sides
Rectangle: a parallelogram with ____________ ____________ angles
Square: a parallelogram with ____________ ________________ sides and ____________ ____________ angles

3. Relationships among Special Parallelograms
The Venn diagram shows the relationships among special parallelograms. Each shape has the properties of every group that it belongs to.
Rhombuses
Rectangles

4. Corollaries about Special Quadrilaterals
Rhombus Corollary: a quadrilateral is a rhombus if and only if it has ____________ congruent ____________
Rectangle Corollary: a quadrilateral is a rectangle if and only if it has ____________ ____________ angles.
Square Corollary: a quadrilateral is a square if and only if it is a _______________ and _______________

5. EX 1: Decide whether the statement is sometimes, always or never true.
A) A rectangle is a parallelogram.
B) A rectangle is a rhombus.
C) A parallelogram is a rhombus.
D) A square is a rectangle.
E) A rhombus is equilateral.
F) The opposite angles of a rhombus are supplementary.

6. EX 2: For any rectangle ABCD, decide whether the statement is always, sometimes, or never true.

7. Diagonals of Special Parallelograms
Theorem 6.13: A parallelogram is a ______________ if and only if its ____________________ are ____________________
Theorem 6.14: A parallelogram is a ______________ if and only if each ____________________ bisects a pair of _______________ angles.
Theorem 6.15: A parallelogram is a ______________ if and only if its ___________________ are ____________________

8. EX 3: Each figure is a parallelogram
EX 3: Each figure is a parallelogram. Identify the special type and explain your reasoning.
A) B)
C) D)

9. EX 4: Find the value of variable(s)
A) MNOP is a Square
B) ABCD is a Rhombus
C) QRST is a Rhombus

10. EX 4: Find the value of x D) EFGH is a Rectangle
E) JKLM is a Rectangle