6.2 parallelograms 2016 ink.notebook. January 11, Page 16. Page Parallelograms. Don't forget to put it in the table of contents

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1 6.2 parallelograms 2016 ink.notebook Page 16 Page Parallelograms Don't forget to put it in the table of contents Lesson Objectives Standards 6.2 Parallelograms Press the tabs to view details. Lesson Notes Lesson Objectives Standards Lesson Notes After this lesson, you should be able to successfully recognize and apply the properties of parallelograms. Press the tabs to view details. 1

2 Lesson Objectives Standards Lesson Notes G.MG.1 Use geometric shapes, their measures, and their properties to describe objects. G.GPE.4 Use coordinates to prove simple geometric theorems algebraically. 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.CO.11 G.CO.12 Prove theorems about parallelograms. Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Parallelogram A quadrilateral in which both pairs of opposite sides are parallel Parallelogram A quadrilateral in which both pairs of opposite sides are parallel Cut this piece off Parallelogram A quadrilateral in which both pairs of opposite sides are parallel Cut this piece off Opposite sides are congruent. Consecutive angles are supplementary Opposite angles are congruent. Diagonals bisect each other. 2. 8x If a parallelogram has 1 rt 's, then it has 4 rt angles. Each diagonal separates the parallelogram into 2 Ë's. A B C ËABC ËDCB D 2

3 Opposite sides are congruent Consecutive angles are supplementary Opposite angles are congruent. 2. 8x 5. Diagonals bisect each other. 112 If a parallelogram has 1 rt 's, then it has 4 rt angles Each diagonal separates the parallelogram into 2 Ë's. A B C D ËABC ËDCB If each quadrilateral is a parallelogram, find the value of each variable x 12 2y Explain why it is impossible for each figure to be a parallelogram

4 If each quadrilateral is a parallelogram, find the value of each variable If each quadrilateral is a parallelogram, find the value of each variable If each quadrilateral is a parallelogram, find the value of each variable

5 Explain why it is impossible for each figure to be a parallelogram On the Worksheet 5

6 Coordinate Geometry. Find the coordinates of the intersection of the diagonal of ABCD with the given vertices. A. A(3, 6), B(5, 8), C(3, 2), and D(1, 4) Coordinate Geometry. Find the coordinates of the intersection of the diagonal of ABCD with the given vertices. B. A( 4, 3), B(2, 3), C( 1, 2), and D( 7, 2) HOMEWORK R 2a S 2b - 1 b + 3 U 3a - 5 T Practice WS on Parallelograms 6

7 Use RSTU to find each measure or value. 7. m RST = Coordinate Geometry. Find the coordinates of the intersection of the diagonal of HJKL with the given vertices. 11. H(1, 1), J(2, 3), K(6, 3), L(5, 1) 8. m STU = 9. m TUR = 10. b = 7

8 Coordinate Geometry. Find the coordinates of the intersection of the diagonal of HJKL with the given vertices. 12. H( 1, 4), J(3, 3), K(3, 2), L( 1, 1) 13. CONSTRUCTION Mr. Rodriquez used the parallelogram at the right to design a herringbone pattern for a paving stone. He will use the paving stone for a sidewalk. If m 1 is 130, find m 2, m 3, and m DISTANCE Four friends live at the four corners of a block shaped like a parallelogram. Gracie lives 3 miles away from Kenny. How far apart do Teresa and Travis live from each other?

9 Answers: 1. 2a = 3a 5, a = 5, 2b 1 = b + 3, b = 4 3. x 2 = 19, x = 21, y + 1 = 26, y = a + 14 = 6a + 4, a = 2, 9b + 8 = 10b + 1, b = (3.5, 2) 13. m 2 = 50, m 3 = 130, m 4 = a 4 = a + 2, a = 3, b + 1 = 2b, b = x 3 = 15, x = 18, y + 3 = 12, y = 9 In the book, do pages , problems: 9 12, 15 20, 46, 47 9

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