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If you missed class today, your notes are waiting for you at Emerge

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Presentation on theme: "If you missed class today, your notes are waiting for you at Emerge"— Presentation transcript:

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 )?

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