Geometry Topic 4 Quadrilaterals and Coordinate Proof

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Geometry Topic 4 Quadrilaterals and Coordinate Proof

MAFS.912.G-CO.3.11 In the diagram below, parallelogram has diagonals and that intersect at point. Which expression is NOT always true? A. B. C. D. C

MAFS.912.G-CO.3.11 Parallelogram with diagonals and intersecting at is shown below. Which statement must be true? A. B. C. D. B

MAFS.912.G-CO.3.11 Which statement is NOT always true about a parallelogram? A. The diagonals are congruent. B. The opposite sides are congruent. C. The opposite angles are congruent. D. The opposite sides are parallel. A

MAFS.912.G-CO.3.11 Which statement is true about every parallelogram? A. All four sides are congruent. B. The interior angles are all congruent. C. Two pairs of opposite sides are congruent. D. The diagonals are perpendicular to each other. C

MAFS.912.G-CO.3.11 Graph the points ( 1,2), (1,8), and (5,2). Find all possible coordinates of the point so that is a parallelogram. B A C (3, -4), (7, 8), (-5, 8)

MAFS.912.G-CO.3.11 If =7 5, =6 +4, = + 6, and =8 + 3, find the values of and for which must be a parallelogram. =9 and =3/4

MAFS.912.G-CO.3.11 A quadrilateral whose diagonals bisect each other and are perpendicular is a A. Rhombus B. Rectangle C. Trapezoid D. Parallelogram A

MAFS.912.G-CO.3.11 Which quadrilateral has diagonals that are always perpendicular bisectors of each other? A. Square B. Rectangle C. Trapezoid D. Parallelogram A

MAFS.912.G-CO.3.11 Use the points shown in the coordinate plane pictured to determine two other points that can be used to form a parallelogram. Justify your solution using properties of parallelograms. Sample answer: Points and can be used as a side or a diagonal of a parallelogram. There are many acceptable solutions that would satisfy the properties of parallelograms. Have students use the distance formula to show that opposite sides are congruent or that diagonals bisect each other. They should use the slope of the sides to verify that opposite sides are parallel.

MAFS.912.G-CO.3.11 Which statement below does NOT prove that quadrilateral is a rhombus? A. AC BD B. The diagonals both bisect opposite angles. C. AB AD DC BC D. DAB DCB D

MAFS.912.G-CO.3.11 In parallelogram, diagonals and intersect at. Which statement does NOT prove parallelogram is a rhombus? A. AC BD B. AB BC C. AC DB D. AC bisects DCB A

MAFS.912.G-CO.3.11 Quadrilateral ABCD is a parallelogram. Jaleel is trying to prove that both pairs of opposite sides of Quadrilateral ABCD are congruent. Complete the proof. Statements Quadrilateral ABCD is a parallelogram and ΔBAC ΔDCA and Given Reasons Definition of parallelogram If two lines are parallel, Alternate Interior Angles are congruent. Reflexive property If two lines are parallel, alternate interior angles are congruent Angle-side-angle (ASA) Corresponding parts of congruent triangles are congruent

MAFS.912.G-CO.3.11 A student in a Geometry class was given this diagram of quadrilateral CDEF. The student wants to prove quadrilateral CDEF is a parallelogram. In the diagram: Six reasons are shown, labeled 1 through 6. 1. Definition of parallelogram 2. Given 3. Side-Side-Side (SSS) 4. Reflexive property of equality 5. Alternate interior angles are equal, so lines are parallel 6. Corresponding parts of congruent triangles are congruent Statements and ΔCDF ΔEFD 1 3and 2 4 and is a parallelogram Reasons 2 4 3 6 5 1

MAFS.912.G-GPE.2.4 Quadrilateral is graphed on the set of axes below. Which quadrilateral best classifies ABCD? A. Trapezoid B. Rectangle C. Rhombus D. Square C

MAFS.912.G-GPE.2.4 Rectangle has vertices (0,4), (4,2), (1, 4), and ( 3, 2). Determine and state the coordinates of the point of intersection of the diagonals. (½, 0)

MAFS.912.G-GPE.2.4 The coordinates of two vertices of square are 2,1 and (4,4). a) Determine the slope of side. = 2 3 b) Write an equation of the line that contains side. = 2 3 +20 3 c) Determine one possible location for vertex. (1,6)or (7,2)

MAFS.912.G-GPE.2.4 The vertices of quadrilateral have coordinates 3,1, 1, 5, 7, 2, and 3,4. a) Prove that is a parallelogram. slope = slope = slope = Opposite sides are parallel, JKLM is a parallelogram. b) Prove that is NOT a rhombus. slope = is NOT congruent to therefore it is NOT a rhombus.

MAFS.912.G-GPE.2.4 Jim is experimenting with a new drawing program on his computer. He created quadrilateral with coordinates 2,3, 5, 4, 2, 1, and (5,6). Jim believes that he has created a rhombus but not a square. Prove that Jim is correct. slope = slope = slope = slope = Opposite sides are parallel, TEAM is a parallelogram. All sides and opposite angles are congruent, the quadrilateral is a rhombus.

MAFS.912.G-GPE.2.4 Given: 4,1, 2, 3, (2, 1). Prove: is an isosceles right triangle. = 20, = 20, = 40 is an isosceles triangle because it has two sides of equal length.

MAFS.912.G-GPE.2.4 Parallelogram has vertices: (1,2), (5,3), (6,6), and (2,5). Point is located on at (1 parallel to.,4). Point lies on such that is Write an ordered pair to represent the location of Point. (5,5)

MAFS.912.G-GPE.2.7 Find the perimeter of the triangle. A. 6+6 2 B. 6 3 2 C. 6+3 2 D. 3 3 2 A

MAFS.912.G-GPE.2.7 Your club is making a banner for an upcoming event. You need to purchase some fabric while staying within your budget. Part A: Calculate the area of your banner based on the given diagram. 18 +18 +64 +4..=104.. 11.55.. Watch unit conversions: each unit is 2 in the diagram; 1.. = 9.. Part B: The fabric you want is $3.99 per square yard. How much will the fabric cost? $3.99 11.55.. $46.08 (Again, watch units: use..) 1 = (2 +4 ) 2 6 =18..=2.. = =..... = =2.. = =..... Continue on next slide

MAFS.912.G-GPE.2.7 Your club is making a banner for an upcoming event. You need to purchase some fabric while staying within your budget. Part C: The banner could use a border. How much material will you need for the border? 4+2+8+2+4+6.32+4+2.82+2.82+4+6.32= 46.28 = 15.43..... Part D: The border material costs $1.25 per yard. If you have $18 left over in the budget, can you afford a border? + =.... + =.... + =... + =... Border costs $1.25 15.43 = $19.29 so no, they do not have enough left in the budget.

MAFS.912.G-GPE.2.7 The diagonals of a rectangle are points A(-4, 1 ) and C(6, -4 ). Determine the area of the rectangle. Verify your answer algebraically. The other two vertices should be plotted at (-4, -4) and (6, 1). The dimensions of the triangle will then be 5 and 10. = = (10)(5) = 50

MAFS.912.G-GPE.2.7 A homeowner wants to fence in the area shown below by hexagon for a garden. The scale of the plan to the actual area is 1 = 5.5. Determine the total number of feet of fencing the homeowner would need to purchase to enclose the entire area. : =2 2 = 3 = 5 = 2 = 10 2 = 32 + 12 2 = 9+1= 10 =2 Total Perimeter =2 2cm +3+5+2+ 10+2 17.99 (17.99 )(5.5) 98.9

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