In the beginning of the class we corrected the homework that was due today:

Most of the questions used the definitions below, that’s why she reviewed them after the homework.

They were:
- Definition of parallelograms: Both pairs of opposite sides are parallel- Theorem 6-1: Opposite sides of a parallelogram are congruent.- Theorem 6-2: Opposite angles of a parallelogram are congruent- Theorem 6-3: Consecutive angles of a parallelogram are supplementary- Theorem 6-4: The diagonals of a parallelogram bisect each other


Many people had problems on doing # 34 and 35, so I’ll explain them now:
34)
N C


Q






M T

And (NQ= 3A + 18) NT=12a QC= a + 2b QM= 3b + 1(that was the given)

NQ=1/2 NT(because the diagonals bisect each other)
So
3a+18=1/2(12a)
3a+18=6a
18=3a
a=6
So if you replace
6+2b=3b+1
5=b












P
35) A B 42
148



S Q



D C


13




Then by using all you know (consecutive angles are supplementary, opposite angles are congruent, etc) you’d find the blue angles. The goal was to get angle APS hint remember the things on the parenthesis.



Then we learned new theorems:

Th 6-6 : If: a quadrilateral has both pairs of opposites angles congruent.
(converse Then: It’s a parallelogram.
of 6-2)

Th 6-7 : If: a quadrilateral has diagonals bisecting each other.
(converse Then: It’s a parallelogram.
of 6-4)

PS: Th 6-3 doesn’t have a converse because it’d affect trapezoids.

Th 6-8 : if: only one pair of opposites sides of a quadrilateral is both parallel and congruent.
Then: it’s a quadrilateral
Ms Saatkamp repeated it like 100 times that is only one PAIR of opposite sides not any side of the figure, she even put stars near this theorem.

Then we learned about rectangles:

Def. It’s a quadrilateral with 4 right angles (PS: it has also the properties of a parallelogram, but the definition still the same, it just needs to be a parallelogram to be a rectangle.)

Th 6-9 : If: a parallelogram is a rectangle
Then: its diagonals are congruent
Th 6-10: If: the diagonals of a parallelogram are congruent
(converse Then: the parallelogram is a rectangle
Of Th 6-9)

Our homework is Page 101 # 15-32 all +page 110 # 15-38 all