6.4 rectangles 2016 ink.notebook. January 22, Page 22. Page Rectangles. Practice with. Rectangles. Standards. Page 24.
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1 6.4 rectangles 2016 ink.notebook Page 22 Page Rectangles Practice with Rectangles Lesson Objectives Standards Lesson Notes Page Rectangles Press the tabs to view details. 1
2 Lesson Objectives Press the tabs to view details. Standards Lesson Notes After this lesson, you should be able to successfully apply the properties of rectangles. 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.). Quadrilaterals A rectangle is a parallelogram with 4 RIGHT ANGLES. ** A rectangle is a special PARALLELOGRAM. The diagonals of a rectangle are. 2
3 6.4 rectangles 2016 ink.notebook A rectangle also has all the properties of a parallelogram. Opposite sides are. Opposite angles are. Opposite sides are congruent. Consecutive angles are supplementary. The diagonals each other. 1. Quadrilateral RUTS is a If US = and RT = 7 2, find. 2. Quadrilateral RUTS is a If mústr = and múutr = 16 9, find mústr. 3
4 3. If AE = 36 and CE = 2 4, find. 4. If BC = 24 and AD = 5y 1, find y. 5. If m BEA = 62, find m BAC 7. If AB = 6y and BC = 8y, find BD in terms of y. 6. If BD = 8y 4 and AC = 7y + 3, find BD. 8. If m AED = 12 and m BEC = , find m AED 4
5 6.4 rectangles 2016 ink.notebook y Determine whether ABCD is a B The vertices are A( 3, 0), B( 2, 3), C(4, 1), and D(3, 2). Use the Slope Formula, C A D If both pairs of opposite sides have the same slope, then it is a parallelogram. If consecutive sides are also perpendicular (negative reciprocals) then it is a y Determine whether ABCD is a The vertices are A( 3, 0), B( 2, 3), C(4, 1), and D(3, 2). B C Use the Distance Formula, If both pairs of opposite sides have the length, then it is a parallelogram. If the diagonals are also congruent, then it is a AC = BD = A D BC = AD = AB = CD = 5
6 On the Worksheet Graph each quadrilateral with the given vertices. Determine whether the figure is a Justify your answer using the indicated formula. 1. A( 3, 1), B( 3, 3), C(3, 3), D(3, 1); Distance Formula y Graph each quadrilateral with the given vertices. Determine whether the figure is a Justify your answer using the indicated formula. 2. A( 3, 0), B( 2, 3), C(4, 5), D(3, 2); y Slope Formula HOMEWORK 6.4 Practice WS on Rectangles 6
7 1. If AC = and DB = 4 1, find DB. 2. If AC = + 3 and DB = 3 19, find AC. 3. If AE = and EC = 5 15, find AC. 4. If DE = 6 7 and AE = 4 + 9, find DB. 7
8 5. If m DAC = and m BAC = find m BAC. 6. If m BDC = and m ADB = 9 7 find m BDC. 7. If m ABD = 7 31 and m CDB = find m ABD. 8. If m BAC = + 3 and m CAD = + 15 find m BAC. 8
9 Graph each quadrilateral with the given vertices. Determine whether the figure is a Justify your answer using the indicated formula. 9. P( 3, 2), Q( 4, 2), R(2, 4), S(3, 0); y Slope Formula Graph each quadrilateral with the given vertices. Determine whether the figure is a Justify your answer using the indicated formula. 10. J( 6, 3), K(0, 6), L(2, 2), M( 4, 1); y Distance Formula Graph each quadrilateral with the given vertices. Determine whether the figure is a Justify your answer using the indicated formula. 11. T(4, 1), U(3, 1), X( 3, 2), Y( 2, 4); y Distance Formula 12. FRAMES Jalen makes the rectangular frame shown. In order to make sure that it is a rectangle, Jalen measures the distances BD and AC. How should these two distances compare if the frame is a rectangle? 9
10 13. SWIMMING POOLS Antonio is designing a swimming pool on a coordinate grid. Is it a rectangle? Eplain Answers: 52 10
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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