1. If you missed class today, your notes are waiting for you at Emerge
If you missed class today, your notes are waiting for you at Emerge. Please let me know if you need to arrange a different way to get them.
For this week:
Please complete the new Grid Words that is at the bottom of the power point. The one in your notes was a bit challenging. If you wish to tackle it, I will help AND offer bonus points. YOU CAN DO IT!
Triangle Sorting and Teaching Textbooks Lesson 55 due Friday
Chapter 7 test due Monday
Lesson 57 due Tuesday
GridWords due next Wednesday in class.
Proof Sheets B and C due in class

2. Quadrilaterals __________ sides ________ vertices _____int. angles
that add up to equal ________0
Label: consecutive sides/angles, opposite sides/angles
TRAPEZOID
Altitude: ______ auxiliary line segment connecting one _________, to the opposite base.
Median: ______ that joins ___________of legs
diagonal: ______ from one _____________ to the other
ISOSCELES TRAPEZOID
______ congruent legs
Lower base angles ______
Upper base angles ______
Diagonals are _________

3. 4 4 Quadrilaterals 4 360 __________ sides ________ vertices
_____int. angles
that add up to equal ________0
Label: consecutive sides/angles, opposite sides/angles 4 4
360
TRAPEZOID
Altitude: ______ auxiliary line segment connecting one _________, to the opposite base.
Median: ______ that joins ___________of legs
diagonal: ______ from one _____________ to the other
ISOSCELES TRAPEZOID
______ congruent legs
Lower base angles ______
Upper base angles ______
Diagonals are _________

4. 4 4 Quadrilaterals 4 OS CS CS CS OS OS 360 CS OS __________ sides
________ vertices
_____int. angles
that add up to equal ________0
Label: consecutive sides/angles, opposite sides/angles 4 4 OS CS CS CS OS OS
360 CS OS
TRAPEZOID
Altitude: ______ auxiliary line segment connecting one _________, to the opposite base.
Median: ______ that joins ___________of legs
diagonal: ______ from one _____________ to the other
ISOSCELES TRAPEZOID
______ congruent legs
Lower base angles ______
Upper base angles ______
Diagonals are _________

5. 4 4 Quadrilaterals 4 OS CS CS CS OS OS 360 CS OS __________ sides
________ vertices
_____int. angles
that add up to equal ________0
Label: consecutive sides/angles, opposite sides/angles 4 4 OS CS CA OA CS CS OS OS CA OA
360 CS OS
TRAPEZOID
Altitude: ______ auxiliary line segment connecting one _________, to the opposite base.
Median: ______ that joins ___________of legs
diagonal: ______ from one _____________ to the other
ISOSCELES TRAPEZOID
______ congruent legs
Lower base angles ______
Upper base angles ______
Diagonals are _________

6. 4 4 Quadrilaterals 4 OS CS CS CS OS OS 360 CS OS __________ sides
________ vertices
_____int. angles
that add up to equal ________0
Label: consecutive sides/angles, opposite sides/angles 4 4 OS CS CA OA CS CS OS OS CA OA
360 CS OS
TRAPEZOID
ONLY 1
base
leg
Altitude: ______ auxiliary line segment connecting one _________, to the opposite base.
Line segment
Median: _______ that joins ___________of legs
midpoint of a pair
leg
base
diagonal: ______ from one _____________ to the other
ISOSCELES TRAPEZOID
______ congruent legs
Lower base angles ______
Upper base angles ______
Diagonals are _________

7. 4 4 Quadrilaterals 4 OS CS CS CS OS OS 360 CS OS __________ sides
________ vertices
_____int. angles
that add up to equal ________0
Label: consecutive sides/angles, opposite sides/angles 4 4 OS CS CA OA CS CS OS OS CA OA
360 CS OS
TRAPEZOID
ONLY 1
base
leg
Altitude: ______ auxiliary line segment connecting one _________, to the opposite base.
PERPENDICULAR
Median: _______ that joins ___________of legs
Line segment
midpoint of a pair
leg
base
base
diagonal: ______ from one _____________ to the other
ISOSCELES TRAPEZOID
______ congruent legs
Lower base angles ______
Upper base angles ______
Diagonals are _________

8. 4 4 Quadrilaterals 4 OS CS CS CS OS OS 360 CS OS __________ sides
________ vertices
_____int. angles
that add up to equal ________0
Label: consecutive sides/angles, opposite sides/angles 4 4 OS CS CA OA CS CS OS OS CA OA
360 CS OS
TRAPEZOID
ONLY 1
INFINITE
base
leg
Altitude: ______ auxiliary line segment connecting one _________, to the opposite base.
PERPENDICULAR
Line segment
Median: _______ that joins ___________of legs
midpoint of a pair
leg
base
base
diagonal: ______ from one _____________ to the other
segment
TWO
vertex
ISOSCELES TRAPEZOID
______ congruent legs
Lower base angles ______
Upper base angles ______
Diagonals are _________

9. 4 4 Quadrilaterals 4 OS CS CS CS OS OS 360 CS OS __________ sides
________ vertices
_____int. angles
that add up to equal ________0
Label: consecutive sides/angles, opposite sides/angles 4 4 OS CS CA OA CS CS OS OS CA OA
360 CS OS
TRAPEZOID
ONLY 1
INFINITE
base
leg
Altitude: ______ auxiliary line segment connecting one _________, to the opposite base.
PERPENDICULAR
Line segment
Median: _______ that joins ___________of legs
midpoint of a pair
leg
base
base
diagonal: ______ from one _____________ to the other
segment
TWO
vertex
ISOSCELES TRAPEZOID
______ congruent legs
Lower base angles ______
Upper base angles ______
Diagonals are _________
TWO

10. 4 4 Quadrilaterals 4 OS CS CS CS OS OS 360 CS OS __________ sides
________ vertices
_____int. angles
that add up to equal ________0
Label: consecutive sides/angles, opposite sides/angles 4 4 OS CS CA OA CS CS OS OS CA OA
360 CS OS
TRAPEZOID
ONLY 1
INFINITE
base
leg
Altitude: ______ auxiliary line segment connecting one _________, to the opposite base.
PERPENDICULAR
Line segment
Median: _______ that joins ___________of legs
midpoint of a pair
leg
base
base
diagonal: ______ from one _____________ to the other
segment
TWO
vertex
ISOSCELES TRAPEZOID
______ congruent legs
Lower base angles ______
Upper base angles ______
Diagonals are _________
TWO
CONGRUENT
CONGRUENT

11. 4 4 Quadrilaterals 4 OS CS CS CS OS OS 360 CS OS __________ sides
________ vertices
_____int. angles
that add up to equal ________0
Label: consecutive sides/angles, opposite sides/angles 4 4 OS CS CA OA CS CS OS OS CA OA
360 CS OS
TRAPEZOID
ONLY 1
INFINITE
base
Altitude: ______ auxiliary line segment connecting one _________, to the opposite base.
PERPENDICULAR
Line segment
leg
Median: _______ that joins ___________of legs
midpoint of a pair
leg
base
base
diagonal: ______ from one _____________ to the other
segment
TWO
vertex
ISOSCELES TRAPEZOID
______ congruent legs
Lower base angles ______
Upper base angles ______
Diagonals are _________
TWO
CONGRUENT
CONGRUENT
CONGRUENT

12. To prove a quadrilateral is a parallelogram...
Diagonals bisect each other
One pair of opposite sides is both parallel &congruent
congruent.
Both pairs of opposite angles
Both pairs of opposite sides are parallel (definition)
or sides are
auxiliary: lines you
can draw inside or out
to help show/prove.
2 points determine
a line
If you draw
one then...

13. If a quadrilateral is a parallelogram...
______________________________________
______________________________________
______________________________________
Two pair of parallel sides
Consecutive angles are supplementary
Both pairs of opposite sides are parallel (definition)
2) Both pairs of opposite angles
are congruent
Both pairs of opposite side are congruent.
4) One pair of opposite sides is
both parallel and congruent
Diagonals bisect each other
______________________________________
auxiliary: lines you
can draw inside or out
to help show/prove.
2 points determine
a line
If you draw
one then...

14. If a quadrilateral is a parallelogram...
______________________________________
______________________________________
Opposite angles are
congruent
______________________________________
Two pair of parallel sides
Consecutive angles are supplementary
Both pairs of opposite sides are parallel (definition)
2) Both pairs of opposite angles
are congruent
Both pairs of opposite side are congruent.
4) One pair of opposite sides is
both parallel and congruent
Diagonals bisect each other
______________________________________
auxiliary: lines you
can draw inside or out
to help show/prove.
2 points determine
a line
If you draw
one then...

15. If a quadrilateral is a parallelogram...
______________________________________
______________________________________
Opposite angles are
congruent
______________________________________
Two pair of parallel sides
Consecutive angles are supplementary
Opposite sides are
congruent
Both pairs of opposite sides are parallel (definition)
2) Both pairs of opposite angles
are congruent
Both pairs of opposite side are congruent.
4) One pair of opposite sides is
both parallel and congruent
Diagonals bisect each other
______________________________________
auxiliary: lines you
can draw inside or out
to help show/prove.
2 points determine
a line
If you draw
one then...

16. If a quadrilateral is a parallelogram...
______________________________________
Opposite angles are
congruent
Two pair of parallel sides
Consecutive angles are supplementary
Opposite sides are
______________________________________
Diagonals bisect
each other
______________________________________
Both pairs of opposite sides are parallel (definition)
2) Both pairs of opposite angles
are congruent
Both pairs of opposite side are congruent.
4) One pair of opposite sides is
both parallel and congruent
Diagonals bisect each other
auxiliary: lines you
can draw inside or out
to help show/prove.
2 points determine
a line
If you draw
one then...

17. Each figure has the same properties as the ones above it!
Quadrilaterals
Parallelogram
trapezoid
isosceles
trapezoid
rectangle
rhombus
square

18. 4 congruent sides and diagonals are perpendicular
Follow the path
Quadrilaterals
2 ___________of parallel sides
both sets of sides are _________
Consecutive angles are _________
Opposite angles are _____________________
______________________ bisect each other
Parallelogram
trapezoids
4 congruent sides and diagonals are perpendicular
rectangle
rhombus
square

19. Quadrilaterals Follow the path trapezoids rectangle rhombus square
2 ___________of parallel sides
both sets of sides are _________
Consecutive angles are _________
Opposite angles are _____________________
______________________ bisect each other
Parallelogram
trapezoids
4 congruent sides and diagonals are perpendicular
rectangle
rhombus
4 congruent sides and 4 right angles
square

20. Quadrilaterals Follow the path trapezoids rectangle rhombus square
Parallelogram
trapezoids
4 congruent sides and diagonals are perpendicular
rectangle
rhombus
4 right angles
square
4 congruent sides and 4 right angles

21. Proof Examples

22. Mastering the Distance Formula
1) Find the length of AC given A( 2 , 3) and C(5, 7).
2) Find the length of AB given A(3, -4) and B(-2, 3).
3) Find the distance between the points ( 1 , 3 ) and (6, 15).
Things that make you go hmmm???
How can you use the distance formula to solve problems like the following one: 4) The point (1,2) lies on a circle. What is the length of the radius of this circle if the center is located at (4,6)?
5) The point ( -2,-1 ) lies on a circle. What is the length of the radius of this circle if the center is located at ( 0, 4 )?
6) The point ( 4 ,5 ) lies on a circle. What is the diameter of this circle if the center is located at ( 7, 9 )?
7) What is the distance between points c(-2,3) and D(0,5)?
8) The point ( 1 ,2 ) lies on a circle. What is the diameter of this circle if the center is located at ( 7, 10 )?