Class Summary 4/12/08 by Guilherme

Today we started things off by going over the homework from page 301, #15-32 all. After Ms. Saatkamp corrected some diagram questions in the homework, we started learning about another type of quadrilateral, Rectangles.

Rectangles

Definition: A quadrilateral with four right angles.
There are two theorems on chapter 16 regarding rectangles especifically, and those are:

Theorem 6-9: If a parallelogram is a rectangle then it's diagonals are congruent.
Explanation: For example, if a parallelogram being a rectangle is given as information then it can be stated than all the diagonal lines in that rectangle is congruent, or equal to each other.

Theorem 6-10: If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.
Explanation: A parallelogram can be considered a rectangle if its diagonals are congruent.


After we got over Rectangles we moved on to Rhombi (Rhombus).

Rhombus

Definition: It's a quadrilateral with all sides congruent.
Unlike Rectangles, they have three theorems especifically for them, and those are:

Theorem 6-11: If it is a rhombus then the diagonals are perpendicular.
Explanation: If the figure given is rhombus then it can be said that its diagonals are perpendicular to each other, eventually forming 90 degree angles.

Theorem 6-12: If a parallelogram has perpendicular diagonals then it is a rhombus.
Explanation: If the figure given is said to be a parallelogram and if that parallelogram has perpendicular diagonals then it is correct to assume that the figure is a rhombus.

Theorem 6-13: If it is a rhombus then each diagonals bisect a pair of opposite angles.
Explanation: If the rhombus is given then its diagonals will bisect (pass through the middle) of a pair (2) of opposite angles in that rhombus.

Then went on to Squares, however we didn't have any theorems on them. Instead, Ms. Saatkamp drew us a very helpful diagram about Quadrilaterals.

PARALLELOGRAMS-

RECTANGLES - RHOMBI


SQUARES


This basically states then all the properties used to identify Parallelograms can also be used to identify Rectangles and Rhombi, apart from their own. Squares are the Quadrilaterals that can be identified with any of the properties used on all the three of the Quadrilaterals above.

Finally we finished it off by copying the homework pages

Page 316 #4
Page 317 #'s 21 through 47 ALL