Example 1: MATH is a parallelogram. Find the values of w, x, y, and z. Write an equation for each and write the property of parallelograms used.

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1 Name: Date: Period: Geometr Notes Parallelograms Fab Five Quadrilateral Parallelogram Diagonal Five Fabulous Facts about Parallelograms: ) ) 3) 4) 5) ***This is the Parallelogram Definition and Theorems! Eample : MTH is a parallelogram. Find the values of w,,, and z. Write an equation for each and write the propert of parallelograms used. M 5 w 55 z H T Eample : Find the values of,, and z. Write the propert of parallelograms used for each. 44 z 05 3 Eample 3: BCD is a parallelogram. Diagonals C and BD intersect at R. If R = 5 + and RC = 3 + 5, find C. Write an equation for each and write the propert of parallelograms used. B R D C

2 Special Parallelograms: Rectangles, Squares and Rhombi Name Date Pd ***Before we add an new properties for a rhombus and a rectangle, remember that each of these shapes has all of the properties that a parallelogram did.*** So mark each of these pictures with the properties of a parallelogram before we add an new ones: R H R E M O T C (Draw in the diagonals, RO and HM ) (Draw in the diagonals, RC and ET ) Rhombus **Diagonals are perpendicular** **Diagonals bisect the corner angles** S Rectangle **Diagonals are congruent** Q U (Draw in the diagonals, Q and SU ) Square **Is also a rhombus (So it has all properties of a rhombus)** **Is also a rectangle (So it has all properties of a rectangle)** Use rhombus PQRS and the given information to find each value.. If SQ = 4, RP = 0, find SR. S R. If m PRS = 7, find m QRS. T 3. Find m STR. 4. If SP = 4 3 and PQ = 8 +, find the value of. P Q Use rectangle RECT and the given information to find each value. R E 5. m RCT = 30, find m ETC. 6. If RC = 5 + and E = + 4, find the value of. T C 7. If m EC = 40, find m EC.

3 Quadrilateral Properties lwas, Sometimes, Never Name Date Pd Using our knowledge of the properties of quadrilaterals, complete each sentence with alwas, sometimes, or never. If ou answer sometimes, describe the cases in which the propert is true.. square is a rhombus.. rhombus is a square. 3. trapezoid is a rectangle. 4. The diagonals of a rhombus are congruent. 5. quadrilateral with one pair of sides congruent and one pair parallel is a parallelogram. 6. rectangle has consecutive sides congruent. 7. The diagonals of a rhombus bisect each other. 8. rectangle has perpendicular diagonals. 9. The diagonals of a parallelogram are perpendicular bisectors of each other. 0. The diagonals of a parallelogram bisect the angles of the parallelogram.. trapezoid has a pair of congruent sides.. The diagonals of a kite are perpendicular. 3. The diagonals of a parallelogram bisect each other. 4. The consecutive angles of a rectangle are congruent and supplementar. 5. Consecutive angles in a parallelogram are congruent. 6. diagonal divides a square into two isosceles right triangles.

4 nswer each of the following questions using our knowledge of parallelograms. 7. QUD is a parallelogram. Find a, b, c, and d. Show our work. a = b = c = d = 8. CRS is a parallelogram. Find each missing angle. C z m R 65 8 n S m = n = = z = 0. portion of isosceles trapezoid NPRT is shown on the grid below. t what coordinates should verte T be placed to make NP parallel to RT in order to complete isosceles trapezoid NPRT? Q D (a, 6) (, b) S (c, d) U (8, 0) 9. Find m, n, and p in the following trapezoid. m = n = p =. t what coordinates should verte Z be placed to create a quadrilateral WXYZ that is similar to quadrilateral PQRS? Given these four equations for lines, sketch the graph. Determine if the will form a quadrilateral and, if so, determine the most precise name of the quadrilateral. Justif our answer.. =, = - + 6, = 4, 3. = 3 4, = - 0, = - = 3 + 6, = - +.

5 Geometr Notes Quadrilaterals from Slopes and Equations of Lines Given: (-4,), M(,4) and R(3,-) Use slope to find the coordinates of point T to form parallelogram MRT. ) T(, ) Given: (-4,), M(,4) and R(3,-) Use slope to find the coordinates of point D to form parallelogram RMD. Name Date Period Given: (-4,), M(,4) and R(3,-) Use slope to find the coordinates of point G to form parallelogram ) D(, ) MRG. 3) G(, ) 4) Given: (-, -) and B(3,3). Use slope to find two sets of coordinates of C and D to make BCD a square. C(, ) and D(, ) or C(, ) and D(, ) 5) Given: (-,-) and C(3,3). Use slope to find the coordinates of B and D so that BCD is a square. B(, ) and D(, ) or B(, ) and D(, ) 6) Given: (-4,), B(0,-), and C(6,4). Use slope to find the coordinates of D so that BCD is a rectangle. D(, ) Given these four equations for lines, sketch the graph. Determine if the will form a quadrilateral and, if the do form a quadrilateral, choose parallelogram, rectangle, rhombus, square, trapezoid, isosceles trapezoid, or kite. Justif our answer. Use our graphing calculator to help verif our answer be sure to Zoom Square.. 7) =3, = 4, = -, and = -4. 8) =, = - + 6, = 4, and = -

6 9) equation of B is = 3 4, equation of BC is = - 0, equation of CD is = 3 + 6, and equation of D is = ) equation of B is = + 3, equation of BC is = - 4, equation of CD is = 3, and equation of D is = - + ) equation of B is = + 3 equation of BC is = equation of CD is = 3 equation of D is = + 3 In the following eercises ou will be given the slope or the length of a side. From that given information, sketch the quadrilateral BCD and choose its most specific name: parallelogram, rhombus, rectangle, square, trapezoid, isosceles trapezoid, or kite. Justif our answer. ) Slope of B = 4, 3) B = 3, BC = 3, CD = 3, 4) Slope of B is -3/4, Slope of BC = -, D = 3, slope of B =, and Slope of BC =, Slope of CD = 4, slope of BC = -/ Slope of CD is -3/4, Slope of D = - Slope of D = -3, D = 4, and BC = 9

7 Geometr Quadrilaterals from Slopes and Equations of Lines Given: (-3,), M(5,4) and R(,-) Use slope to find the coordinates of point T to form parallelogram MRT. ) T(, ) Given: (-3,), M(5,4) and R(,-) Use slope to find the coordinates of point D to form parallelogram RMD. ) D(, ) Name Date Period 3) Given: W(-3, -3), X(, -6), and Y(5, -3). Use slope to find the coordinates of Z so that WXYZ is a rhombus. Z(, ) 4) Given: (-,4), B(,0), and C(5,3). Use slope to find the coordinates of D so that BCD is a rectangle. D(, ) 5) Given C(-, ), D(-5, -3), and E(-4, -0). Use slope & distance to find the coordinates of F so that CDEF is an isosceles trapezoid. F(, ) 6) Given: R(0, 0), (5, 5), I(8, 4). Use distance to find the coordinates of N so that RIN is a kite. N(, ) Given these four equations for lines, sketch the graph. Determine if the will form a quadrilateral and, if the do form a quadrilateral, choose parallelogram, rectangle, rhombus, square, trapezoid, isosceles trapezoid, or kite. Justif our answer. Use our graphing calculator to help verif our answer be sure to Zoom Square.. 9) equation of B is = 5, 0) equation of B is = 3, ) equation of B is = + 3 equation of BC is = -3 0, 3 equation of CD is = + 6, and equation of BC is = + 4, equation of BC is = equation of D is = equation of CD is = + 6, equation of CD is = 3 3 and equation of D is = equation of D is = 4 + 5

8 6-6 Placing Figures in the Coordinate Plane Geometr Tetbook Pg 360 # 0, Give the coordinates for points S and T without using an new variables. Then find the midpoint and the slope of ST. 0. rectangle. parallelogram Pg 346 #9. (modified) Find the coordinates for B so run c run c that the lines and are perpendicular. Hint: the slope of O is so the slope of OB must be. rise d rise d The figure is centered over the origin, so vertices can be found b reflecting over the - or -ais. Opposite sides must have the same slope to be parallel. Slope from (0,0) to (c,d) is rise d run c, or d/c. Use same slope from (b,0) to get T: (b run c, 0 rise d) = (b + c, 0 + d) = (b + c, d) Geometr Tetbook Pg 344 # -7, -5, 9 Practice: Give coordinates for points W and Z without using an new variables.. rectangle 3. square 4. square 5. parallelogram 6. rhombus 7. isosceles trapezoid Give the coordinates for point P without using an new variables. 3. isosceles trapezoid 4. trapezoid with a right angle 5. kite. The coordinates of three vertices of a rectangle are (-a, 0), (a, 0), and (a, b).what are the coordinates of the midpoint of the diagonal joining one of these points with the fourth verte? a. (0, b) b. (0, b) c. (a, b) d. (-a, b)