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Notes: QUADRILATERALS ON A COORDINATE PLANE For items a – k, check the box if the property is true for each classification of parallelograms. CLASSIFICATION PROPERTIES a. The opposite sides are parallel. b. The opposite sides are congruent. c. The opposite angles are congruent. d. The consecutive angles are supplementary. e. The diagonals bisect each other f. It has four right angles g. The diagonals are congruent. i. It has four congruent sides j. The diagonals are perpendicular. k. The diagonals bisect opposite angles. RECTANGLES RHOMBI SQUARES For #1 – 2, refer to the table completed properties above. 1. What do you know about the angles of ALL parallelograms? ______________________________________________________________________________________________ ______________________________________________________________________________________________ ______________________________________________________________________________________________ 2. What do you know about the sides of ALL parallelograms? ______________________________________________________________________________________________ ______________________________________________________________________________________________ ______________________________________________________________________________________________ Geometry Unit 7- Properties of Polygons Page 473 Notes: QUADRILATERALS ON A COORDINATE PLANE TERM DESCRIPTION EXAMPLE HOW TO NAME IT Two coplanar lines that never __________ and have the _________ slope. l ||m Two lines that intersect to form four __________ angles and have slopes that are ____________ ____________. l m Slope is RISE over RUN. EXAMPLE 1: Determine if quadrilateral ABCD is a parallelogram by proving whether or not both pairs of opposite sides are parallel. Slope of AB : _________ Slope of DC : _________ Parallel? Yes or No Slope of BC : _________ Slope of AD : _________ Parallel? Yes or No How do you know if the opposite sides are congruent? ______________________________________________________________________ ______________________________________________________________________ Is quadrilateral ABCD is a parallelogram? Yes or No How do you know? _____________________________________________________ ____________________________________________________________________ Geometry Unit 7- Properties of Polygons Page 474 Notes: QUADRILATERALS ON A COORDINATE PLANE EXAMPLE 2: Determine the most specific classification of parallelogram ABCD. Slope of AB : _________ Slope of CB : _________ Perpendicular? Yes or No or No or No Slope of DC : _________ Slope of DA : _________ Perpendicular? Yes Slope of CA : _________ Slope of DB : _________ Perpendicular? Yes How do you know if the opposite sides are congruent? ______________________________________________________________________ ______________________________________________________________________ How do you know if the diagonals are congruent? ______________________________________________________________________ ______________________________________________________________________ What is the most specific classification of parallelogram ABCD? __________________ How do you know? _____________________________________________________ _____________________________________________________________________ Geometry Unit 7- Properties of Polygons Page 475 Notes: QUADRILATERALS ON A COORDINATE PLANE The two-dimensional coordinate system has four quadrants: Quadrant I: (positive, positive) Quadrant II: (negative, positive) Quadrant III: (negative, negative) Quadrant IV: (positive, negative) II I III IV EXAMPLE 3: Plot the parallelogram as described. Three vertices of a parallelogram have coordinates (1, -1), (3, 8) and (5, 0). What are the coordinates of the second-quadrant vertex? ( ______ , ______ ) QUICK CHECK: Plot the parallelogram as described. Three vertices of a parallelogram have coordinates (0, 1), (3, 7) and (4, 4). What are the coordinates of the fourth-quadrant vertex? ( ______ , ______ ) Geometry Unit 7- Properties of Polygons Page 476 Notes: QUADRILATERALS ON A COORDINATE PLANE For items a – e, check the box if the property is true for each classification of quadrilaterals. CLASSIFICATION PROPERTIES a. It has exactly one pair of parallel sides. b. The median is equal to ½ (b1 + b2). c. The legs are congruent. d. The diagonals are congruent. e. The base angles are congruent. TRAPEZOID ISOSCELES TRAPEZOID EXAMPLE 4: A portion of isosceles trapezoid WXYZ X is shown on the grid. At what coordinates should vertex Z be placed to make XY parallel to WZ? W Y Slope of XY : _________ Length of WX : _________ Z (_____ , _____) QUICK CHECK: Which of the following points will complete isosceles trapezoid QRPN? A. R (-2, 3) B. R (0, 4) C. R (2, 7) D. R (4, 9) Geometry Unit 7- Properties of Polygons Page 477 Notes: QUADRILATERALS ON A COORDINATE PLANE The slope-intercept equation of a line is y = mx + b. EXAMPLE 5: Determine the equations of the line that will contain AB in each of the figures. a. c. C D D B C A A B y = ______________________ b. y = ______________________ d. B C A D C D A B y = ______________________ Geometry Unit 7- Properties of Polygons y = ______________________ Page 478