6.3 proving parallelograms day ink.notebook. January 17, Page 20 Page Prove Parallelogram Using Coordinate Geometry.

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1 6.3 proving parallelograms da ink.notebook Januar 17, 2017 Page 20 Page Prove Using oordinate Geometr Lesson Objectives Standards Lesson Notes 6.3 Proving s Lesson Objectives Standards Lesson Notes fter this lesson, ou should be able to successfull prove a figure is a parallelogram. a 2 Press the tabs to view details. Press the tabs to view details. 1

2 6.3 proving parallelograms da ink.notebook Januar 17, 2017 etermine whether is a parallelogram. ( 2, 3), (3, 2), (2, 1), and ( 3, 0). Lesson Objectives Standards Lesson Notes Use the, G.MG.1 Use geometric shapes, their measures, and their properties to describe objects. G.GPE.4 Use coordinates to prove simple geometric theorems algebraicall. G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). G.O.11 Prove theorems about parallelograms. If both pairs of opposite sides have the same slope, then the are parallel and the figure is a parallelogram b definition. Use the istance Formula, If both pairs of opposite sides have the length, then the are congruent and the figure is a parallelogram. quad with opp sides fl. Use the istance and, Find the slopes and lengths of ONE pair of opposite sides. If the slopes are the same, the are parallel. If the lengths are the same, the are congruent and the figure is a parallelogram. quad with opp sides «& fl. = = = = = = Use the Midpoint Formula, Midpoint of = Find the midpoint of the 2 diagonals. If the are the same, then the diagonals bisect each other and figure is a parallelogram. Midpoint of = quad with diagonals bisecting each other fl. etermine whether is a parallelogram. ( 2, 3), (3, 2), (2, 1), and ( 3, 0). Use oordinate Geometr to Prove Use the, etermine whether is a parallelogram. ( 2, 3), (3, 2), (2, 1), and ( 3, 0). Use oordinate Geometr to Prove istance Formula Use the istance Formula, = = If both pairs of opposite sides have the same slope, then the are parallel and the figure is a parallelogram b definition. If both pairs of opposite sides have the length, then the are congruent and the figure is a parallelogram. = quad with opp sides fl. = 2

3 6.3 proving parallelograms da ink.notebook etermine whether is a parallelogram. ( 2, 3), (3, 2), (2, 1), and ( 3, 0). Use oordinate Geometr to Prove Slope N istance Formula Januar 17, 2017 ( 2, 3), (3, 2), (2, 1), and ( 3, 0). Use oordinate Geometr to Prove Midpoint Formula Use the Midpoint Formula, Use the istance and, Find the slopes and lengths of ONE pair of opposite sides. If the slopes are the same, the are parallel. If the lengths are the same, the are congruent and the figure is a parallelogram. quad with opp sides Ç & ß ã. = = etermine whether is a parallelogram. Find the midpoint of the 2 diagonals. If the are the same, then the diagonals bisect each other and figure is a parallelogram. Midpoint of = Midpoint of = quad with diagonals bisecting each other ß ã. whether the figure is a parallelogram. Justif our answer with the 1. (0, 0), (1, 3), (5, 3), (4, 0) 3

4 6.3 proving parallelograms da ink.notebook whether the figure is a parallelogram. Justif our answer with the 2. R( 1, 0), S(3, 0), T(2, 3), U( 3, 2) istance Formula Januar 17, 2017 whether the figure is a parallelogram. Justif our answer with the 3. ( 3, 2), ( 1, 4), (2, 1), (0, 1) istance and s whether the figure is a parallelogram. Justif our answer with the 4. F(3, 3), G(1, 2), H( 3, 1), I( 1, 4) Midpoint Formula 4

5 6.3 proving parallelograms da ink.notebook Januar 17, 2017 HOMEWORK On the Worksheet 6.3 Practice WS Tests for s 1. STREET LMPS When a coordinate plane is placed over the Harrisville town map, the four street lamps in the center are located as shown. o the four lamps form the vertices of a parallelogram? Eplain. whether the figure is a parallelogram. Justif our answer with the 2. P(0, 0), Q(2, 4), S(6, 4), Y(4, 0); 5

6 6.3 proving parallelograms da ink.notebook Januar 17, 2017 whether the figure is a parallelogram. Justif our answer with the 3. W(2, 5), R(3, 3), Y( 2, 3), N( 3, 1); Midpoint Formula whether the figure is a parallelogram. Justif our answer with the 4. S( 2, 1), R(1, 3), T(2, 0), Z( 1, 2); istance and s whether the figure is a parallelogram. Justif our answer with the 5. P( 5, 1), S( 2, 2), F( 1, 3), T(2, 2); whether the figure is a parallelogram. Justif our answer with the 6. ( 2, 4), (5, 4), (8, 1), ( 1, 1); 6

7 6.3 proving parallelograms da ink.notebook Januar 17, 2017 whether the figure is a parallelogram. Justif our answer with the 7. W( 5, 4), X(3, 4), Y(1, 3), Z( 7, 3); Midpoint Formula whether the figure is a parallelogram. Justif our answer with the 8. ( 3, 4), (4, 5), (5, 1), ( 2, 2); whether the figure is a parallelogram. Justif our answer with the 9. J( 4, 4), K( 3, 1), L(4, 3), M(3, 3); etermine if each quadrilateral is a parallelogram. Justif our answer

8 6.3 proving parallelograms da ink.notebook Januar 17, 2017 etermine if each quadrilateral is a parallelogram. Justif our answer etermine if each quadrilateral is a parallelogram. Justif our answer nswers: 8

October 16, proving lines parallel ink.notebook. page Prove Lines Parallel. page 113. Standards. page 115.

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