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Coordinate proofs 2
Coordinate proofs Using the coordinate system to prove something. Coordinate proofs Using the coordinate system to prove something. When we prove something, we need to do it for the general case... 3
Coordinate proofs Using the coordinate system to prove something. When we prove something, we need to do it for the general case... If we work with specific cases, we're just playing with inductive reasoning......we can't prove anything true using inductive reasoning. Coordinate proofs Using the coordinate system to prove something. When we prove something, we need to do it for the general case... If we work with specific cases, we're just playing with inductive reasoning......we can't prove anything true using inductive reasoning. So we use points with variables rather than specific numbers. 4
Coordinate proofs Using the coordinate system to prove something. When we prove something, we need to do it for the general case... If we work with specific cases, we're just playing with inductive reasoning......we can't prove anything true using inductive reasoning. So we use points with variables rather than specific numbers. Yesterday's exercise is an example: ACEO is a quadrilateral It is NOT a specific quadrilateral It could be ANY quadrilateral y T A (2a, 2b) W C (2c, 2d) V what we proved is true for ALL quads O U E (2e, 0) x Coordinate proofs guidelines How can we place our shape on the coordinate graph and make our work a lot easier? 5
Coordinate proofs guidelines How can we place our shape on the coordinate graph and make our work a lot easier? Positioning... Coordinate proofs guidelines How can we place our shape on the coordinate graph and make our work a lot easier? Positioning... Coordinates... 6
Coordinate proofs guidelines How can we place our shape on the coordinate graph and make our work a lot easier? Positioning... Center figure on the origin if it is regular... or... Place a vertex at the origin, side(s) on the axis Coordinates... Coordinate proofs guidelines How can we place our shape on the coordinate graph and make our work a lot easier? Positioning... Center figure on the origin if it is regular... or... Place a vertex at the origin, side(s) on the axis Coordinates... Use coords that are multiples of 2 (especially if finding midpts) 7
Coordinate proof Coordinate proof Draw and label the figure... 8
Coordinate proof R A T P Coordinate proof R A...the midseg too... T P 9
Coordinate proof R A M N T P Coordinate proof R A...give the vertices easy coords to work with... T M N P 10
Coordinate proof R A M N T(0, 0) P Coordinate proof R A M N T(0, 0) P (2a, 0) 11
Coordinate proof R (2b, 2c) A M N T(0, 0) P (2a, 0) Coordinate proof M R (2b, 2c) A (2d, 2c) N T(0, 0) P (2a, 0) 12
Coordinate proof M R (2b, 2c) A (2d, 2c) N T(0, 0) P (2a, 0) Coordinate proof R (2b, 2c) A (2d, 2c) Determine coords of the midseg M T(0, 0) N P (2a, 0) 13
Coordinate proof R (2b, 2c) A (2d, 2c) M (b, c) N T(0, 0) P (2a, 0) Coordinate proof R (2b, 2c) A (2d, 2c) M (b, c) N (a+d, c) T(0, 0) P (2a, 0) 14
Coordinate proof R (2b, 2c) A (2d, 2c) M (b, c) N (a+d, c) T(0, 0) P (2a, 0) Coordinate proof R (2b, 2c) A (2d, 2c) M (b, c) N (a+d, c) Determine slope of MN, RA & TP... T(0, 0) P (2a, 0) 15
Coordinate proof R (2b, 2c) A (2d, 2c) M (b, c) N (a+d, c) Determine slope of MN, RA & TP... T(0, 0) P (2a, 0) Coordinate proof R (2b, 2c) A (2d, 2c) M (b, c) N (a+d, c) Determine slope of MN, RA & TP... T(0, 0) P (2a, 0) Determine length of MN, RA & TP... 16
Coordinate proof R (2b, 2c) A (2d, 2c) M (b, c) N (a+d, c) Determine slope of MN, RA & TP... T(0, 0) P (2a, 0) Determine length of MN, RA & TP... Theorem 6-18: Trapezoid Midseg Thm 1) Midseg of trapezoid is ΙΙ to both bases... MN ΙΙ RA and MN ΙΙ TP 2) Length of midseg is half sum base lengths... R A M N T P 17
Some Algebra review... Some Algebra review... 18
Some Algebra review... Some Algebra review... 19
Some Algebra review... Some Algebra review... 20
Some Algebra review... Some Algebra review... 21
Some Algebra review... Some Algebra review... 22
Some Algebra review... Some Algebra review... 23
Some Algebra review... Some Algebra review... 24
Some Algebra review... Some Algebra review... 25
Some Algebra review... Some Algebra review... 26
Some Algebra review... Some Algebra review... 27
Some Algebra review... 28
L6-7 HW Problems L6 7 Pg 333 #1 3, 5, 6, 9, 25, 26, 30, 31, 42 44 Extra Credit Worksheet (available online) 29