Section 6.4 rhombuses, rectangles and squares

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6.4 Rhombuses, Rectangles, and Squares

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Presentation transcript:

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.

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

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

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 _______________

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.

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

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 ____________________

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)

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

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