6.5 ­ Conditions for Rhombuses, Rectangles, and Squares.notebook
6.5: Conditions for Rhombuses, Rectangles, & Squares
February 02, 2017
Date: 2/2
The following theorems are converses of lesson 6.4. Each theorem
allows you to prove that a parallelogram is either a rhombus or a
rectangle.
Theorem 6­16: “If the diagonals of a parallelogram are perpendicular
then the parallelogram is a rhombus."
Theorem 6­17: “If one diagonal of a parallelogram bisect a pair of
opposite angles, the parallelogram is a rhombus."
Theorem 6­18: “If the diagonals of a parallelogram are congruent
then the parallelogram is rectangle."
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6.5 ­ Conditions for Rhombuses, Rectangles, and Squares.notebook
February 02, 2017
*Notice that if a parallelogram is both a rectangle and a rhombus,
then it is a square
Ex 1). Can you conclude that the parallelogram is a rhombus,
rectangle, or square? Explain.
a)
b)
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6.5 ­ Conditions for Rhombuses, Rectangles, and Squares.notebook
February 02, 2017
Ex 2). For what value of x is ABCD a square?
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6.5 ­ Conditions for Rhombuses, Rectangles, and Squares.notebook
February 02, 2017
Ex 3). For what value of x is DEFG a rhombus?
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6.5 ­ Conditions for Rhombuses, Rectangles, and Squares.notebook
February 02, 2017
Ex 4). LN = 54. For what values of x is LMNO a rectangle?
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6.5 ­ Conditions for Rhombuses, Rectangles, and Squares.notebook
Ex 5). For what value of x is RSTU a rhombus? What is
What is
February 02, 2017
?
?
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6.5 ­ Conditions for Rhombuses, Rectangles, and Squares.notebook
February 02, 2017
Homework:
pg. 407 #1 – 5, 8 – 13, 16 – 18, 23 – 29
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