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6 Quadrilaterals and Angle Sums Practice (pg 2) KEY Practice Problems Use your knowledge of Triangle and Quadrilateral angle sums to complete the table below. Given Find m EAB=95 o m ABC=104 o m 8= 18º m 9= 115º m BED=80 o AC CD m 10= 60º m 11= 82º m 1=83 o m 2=62 o m 12= 100º m 13= 97º m 3=101 o m 4=104 o m 14= 93º m 15= 75º m 5=46 o m 6=70 o m 16= 35º m 17= 17º m 7=35 o m 18= 32º m 19= 14º B 16 A C 1 E G D F 2007, TESCCC Revised 10/01/07 page 6 of 50

8 Quadrilaterals and Angle Sums Practice (pg 2) Practice Problems Use your knowledge of Triangle and Quadrilateral angle sums to complete the table below. Given Find m EAB=95 o m ABC=104 o m 8= m 9= m BED=80 o AC CD m 10= m 11= m 1=83 o m 2=62 o m 12= m 13= m 3=101 o m 4=104 o m 14= m 15= m 5=46 o m 6=70 o m 16= m 17= m 7=35 o m 18= m 19= B 16 A C 1 E G D F 2007, TESCCC Revised 10/01/07 page 8 of 50

10 All in the Family (pg 2) KEY 2. The figure below is a rectangle. A rectangle is a type of quadrilateral that has four right angles. H I K J suur suur suur suur a. Use you pencil and a straightedge to draw lines HI, KJ, and HK. Let HK be a transversal for the other two. What conclusions can you make about lines suur suur HI and KJ based on your knowledge of lines and transversals? Explain. See student drawings suur suur KHI and HKJ are supplementary; therefore, HI KJ. b. Use your pencil to draw sur suur suur sur IJ. Let KJ be a transversal for HK and IJ. What conclusions suur sur can you make about lines HK and IJ based on your knowledge of lines and transversals? Explain. suur sur HKJ and KJI are supplementary; therefore, HK IJ. c. What does your findings from part a and b lead you to believe about the rectangle? The rectangle is also a parallelogram. d. Use a straightedge and your pencil to draw the diagonals of the rectangle. Use patty paper tracings to compare the lengths of the two diagonals. What appears to be true? See student drawing The diagonals appear to be congruent. 2007, TESCCC Revised 10/01/07 page 10 of 50

12 All in the Family (pg 4) KEY 4. The figure below is a square. A square is a type of quadrilateral that has four right angles and four congruent sides. W X Z Y a. Based on the previous explorations, what conclusions can you make about the square? Explain your reasoning. Since the square has four right angles it is also a rectangle. Since the square has four congruent sides it is also a rhombus. Since the rectangle and rhombus are both types of parallelograms, the square is also a parallelogram. 5. Based on the previous explorations, what similarities did you discover about the parallelogram, rectangle, rhombus, and square? Similarities All are parallelograms Rectangle and square have 4 right angles Square and rhombus have 4 congruent sides Rectangle and square have congruent diagonals Square and rhombus have perpendicular diagonals 2007, TESCCC Revised 10/01/07 page 12 of 50

14 All in the Family (pg 6) KEY 7. The figure below is a special type of trapezoid called an Isosceles Trapezoid. An Isosceles Trapezoid has exactly one pair of congruent sides. T R P A a. Use a straightedge and a piece of patty paper to trace the trapezoid. Label the vertices on your tracing. Fold and crease the patty paper so that point T and R coincide. See student samples b. Based on your folding, what can you conclude about the parts of the trapezoid? T Rand P A. c. Based on you findings in part a and b, write a conjecture about isosceles trapezoids. In an isosceles trapezoid, pairs of base angles are congruent. 2007, TESCCC Revised 10/01/07 page 14 of 50

15 All in the Family (pg 7) KEY 8. The figure below is a type of quadrilateral called a Trapezium. A trapezium is a quadrilateral with no pairs of parallel sides. P Q R a. A special type of trapezium is a kite. A kite is a trapezium with two pairs of congruent adjacent sides. The figure below is a kite. K S E I T b. Use a piece of patty paper and a straightedge to trace the kite. Label the vertices of the kite. Use a straightedge to draw the diagonals of the kite on your patty paper tracing. See student samples c. Use a protractor to measure the angles formed by the intersection of the diagonals. Record the measures on your patty paper tracing. What conclusion can you make about the diagonals of the kite? The diagonals of a kite are perpendicular. d. Fold and crease your patty paper tracing so that E coincides sur with I. Examine the crease in your paper. What does this verify about diagonal EI? KT bisects EI. 2007, TESCCC Revised 10/01/07 page 15 of 50

17 All in the Family (pg 2) 2. The figure below is a rectangle. A rectangle is a type of quadrilateral that has four right angles. H I K J suur suur suur suur a. Use you pencil and a straightedge to draw lines HI, KJ, and HK. Let HK be a transversal for the other two. What conclusions can you make about lines suur suur HI and KJ based on your knowledge of lines and transversals? Explain. b. Use your pencil to draw sur suur suur sur IJ. Let KJ be a transversal for HK and IJ. What conclusions suur sur can you make about lines HK and IJ based on your knowledge of lines and transversals? Explain. c. What does your findings from part a and b lead you to believe about the rectangle? d. Use a straightedge and your pencil to draw the diagonals of the rectangle. Use patty paper tracings to compare the lengths of the two diagonals. What appears to be true? 2007, TESCCC Revised 10/01/07 page 17 of 50

19 All in the Family (pg 4) 4. The figure below is a square. A square is a type of quadrilateral that has four right angles and four congruent sides. W X Z Y a. Based on the previous explorations, what conclusions can you make about the square? Explain your reasoning. 5. Based on the previous explorations, what similarities did you discover about the parallelogram, rectangle, rhombus, and square? 2007, TESCCC Revised 10/01/07 page 19 of 50

21 All in the Family (pg 6) 7. The figure below is a special type of trapezoid called an Isosceles Trapezoid. An Isosceles Trapezoid has exactly one pair of congruent sides. T R P A a. Use a straightedge and a piece of patty paper to trace the trapezoid. Label the vertices on your tracing. Fold and crease the patty paper so that point T and R coincide. b. Based on your folding, what can you conclude about the parts of the trapezoid? c. Based on you findings in part a and b, write a conjecture about isosceles trapezoids. 2007, TESCCC Revised 10/01/07 page 21 of 50

22 All in the Family (pg 7) 8. The figure below is a type of quadrilateral called a Trapezium. A trapezium is a quadrilateral with no pairs of parallel sides. P Q R a. A special type of trapezium is a kite. A kite is a trapezium with two pairs of congruent adjacent sides. The figure below is a kite. K S E I T b. Use a piece of patty paper and a straightedge to trace the kite. Label the vertices of the kite. Use a straightedge to draw the diagonals of the kite on your patty paper tracing. c. Use a protractor to measure the angles formed by the intersection of the diagonals. Record the measures on your patty paper tracing. What conclusion can you make about the diagonals of the kite? d. Fold and crease your patty paper tracing so that E coincides sur with I. Examine the crease in your paper. What does this verify about diagonal EI? 2007, TESCCC Revised 10/01/07 page 22 of 50

23 Properties of Quadrilaterals (KEY) Properties of convex quadrilaterals: Have four sides. Have four vertices and angles. Sum of the angles equals 360 o. Are congruent if their corresponding angles and corresponding sides are congruent. Quadrilaterals are generally classified by the number of parallel sides they contain. Study the definitions below. Trapezium a quadrilateral with no pairs of parallel sides o Kite two congruent pairs of adjacent sides Property- Diagonals are perpendicular. One of the diagonals bisects the other. Trapezoid a quadrilateral that has only one pair of parallel sides o Isosceles trapezoid non parallel legs are congruent Property- The base angles of an isosceles trapezoid are congruent. Parallelogram a quadrilateral with two pair of parallel sides, opposite sides are parallel Properties- Opposite sides of a parallelogram are congruent. Opposite angles of a parallelogram are congruent. Consecutive angles of a parallelogram are supplementary. The diagonals of a parallelogram bisect each other. o Rectangle parallelogram with four right angles Property- The diagonals of a rectangle are congruent. o Rhombus parallelogram with four congruent sides Property- The diagonals of a rhombus are perpendicular to each other. o Square parallelogram with four right angles and four congruent sides Practice Problems 1. Write a proof for the statement, Consecutive angles of a parallelogram are supplementary. Extend lines through the opposite sides of a parallelogram. Let one of the other sides be a transversal for the opposite sides. Since the opposite sides are parallel, the pair of same side interior angles formed is supplementary. The same side interior angles formed is a consecutive pair for the parallelogram. 2007, TESCCC Revised 10/01/07 page 23 of 50

24 Properties of Quadrilaterals (pg 2) KEY 2. Write a proof for the statement, The diagonals of a rhombus are perpendicular. R B H Since a rhombus is a parallelogram, the diagonals bisect each other. Therefore, ΔMBR ΔHBR by SSS, and MBR HBR by CPCTC. Since MBR and HBR are congruent and form a linear pair, each has a measure of 90º; therefore, RO MH (the diagonals are perpendicular). M O 2007, TESCCC Revised 10/01/07 page 24 of 50

25 Properties of Quadrilaterals (pg 3) KEY 3. In the parallelogram below, PG = 2x 7, MR = x + 5, and MG = 2x 5. Find the value of x and the PG, MR, and MG. P G M R x = 12, PG = 17, MR = 17, MG = Use the information in the rectangle below to find the value of x, the value of y, TE, RC, RX, EX, TX, and CX. R x E y P 3 T 4 C x = 4, y = 3, TE = 5, RC = 5, RP = EP = TP = CP = , TESCCC Revised 10/01/07 page 25 of 50

26 Properties of Quadrilaterals (pg 4) KEY 5. Given the formula for the area of a triangle, A triangle = ½(base)(height), use the properties of quadrilaterals to derive the formula for the area of a rhombus in terms of its diagonals. Triangle 1 Triangle 2 d 2 d 1 Since the rhombus is a parallelogram, the diagonals bisect each other resulting in four congruent triangles by SSS. Since the diagonals are perpendicular, the triangles are right 1 triangles. The legs of each triangle are 1 2 d and 1 d 2 ; and, the area of one of the triangles is 2 1 ( 1 d1)( 1 d 1 2) = d1d2. Therefore, the area of all four triangles (the rhombus) is ( 1 2) 8 dd = dd. 2007, TESCCC Revised 10/01/07 page 26 of 50

27 Properties of Quadrilaterals (pg 5) KEY 6. Suppose a carpenter is framing a rectangular room and wants to verify that the 4-sided room is square (meaning each corner forms a right angle). What might the carpenter do to verify that each corner forms a right angle without measuring the angles? Assuming opposite sides are congruent, the carpenter could measure the lengths of the diagonals and adjust the framing until each diagonal is the same length, since diagonals of a rectangle are congruent. 7. Suppose a room is constructed in the shape of a rhombus so that one diagonal is 6 ft. long and the other is 8 ft. long. Find the perimeter of the rhombus. The perimeter is 20 ft. 2007, TESCCC Revised 10/01/07 page 27 of 50

28 Properties of Quadrilaterals (pg 6) KEY 8. Use the information in the trapezoid below to find the value of x, the value of y, m T, m R,and m P. X= 5, y = 20, m T = 120, m P= 60, and m R= 100 T (12x+60)º (5y)º R P (4x+40)º 80º A 9. Suppose the length of EI is 10 ft. Use the information in the kite below to find the perimeter of the kite. Perimeter is ( ) 27.1ft. K 45º 45º E 60º I 30º T 10. Use the information in the trapezoid below to find HK, IJ, m KHI HK = 12, IJ= 12, m KHI = 120, m KJI = 60, m HIJ = 120 H 6 3 I, m KJI and m HIJ. K 60º J 2007, TESCCC Revised 10/01/07 page 28 of 50

29 Properties of Quadrilaterals Properties of convex quadrilaterals: Have four sides. Have four vertices and angles. Sum of the angles equals 360 o. Are congruent if their corresponding angles and corresponding sides are congruent. Quadrilaterals are generally classified by the number of parallel sides they contain. Study the definitions below. Trapezium a quadrilateral with no pairs of parallel sides o Kite two congruent pairs of adjacent sides Property- Diagonals are perpendicular. One of the diagonals bisects the other. Trapezoid a quadrilateral that has only one pair of parallel sides o Isosceles trapezoid non parallel legs are congruent Property- The base angles of an isosceles trapezoid are congruent. Parallelogram a quadrilateral with two pair of parallel sides, opposite sides are parallel Properties- Opposite sides of a parallelogram are congruent. Opposite angles of a parallelogram are congruent. Consecutive angles of a parallelogram are supplementary. The diagonals of a parallelogram bisect each other. o Rectangle parallelogram with four right angles Property- The diagonals of a rectangle are congruent. o Rhombus parallelogram with four congruent sides Property- The diagonals of a rhombus are perpendicular to each other. o Square parallelogram with four right angles and four congruent sides Practice Problems 1. Write a proof for the statement, Consecutive angles of a parallelogram are supplementary. 2007, TESCCC Revised 10/01/07 page 29 of 50

30 Properties of Quadrilaterals (pg 2) 2. Write a proof for the statement, The diagonals of a rhombus are perpendicular. R H B M O 2007, TESCCC Revised 10/01/07 page 30 of 50

31 Properties of Quadrilaterals (pg 3) 3. In the parallelogram below, PG = 2x 7, MR = x + 5, and MG = 2x 5. Find the value of x and the PG, MR, and MG. P G M R 4. Use the information in the rectangle below to find the value of x, the value of y, TE, RC, RX, EX, TX, and CX. R x E y P 3 T 4 C 2007, TESCCC Revised 10/01/07 page 31 of 50

32 Properties of Quadrilaterals (pg 4) 5. Given the formula for the area of a triangle, A triangle = ½(base)(height), use the properties of quadrilaterals to derive the formula for the area of a rhombus in terms of its diagonals. Triangle 1 Triangle 2 d 2 d , TESCCC Revised 10/01/07 page 32 of 50

33 Properties of Quadrilaterals (pg 5) 6. Suppose a carpenter is framing a rectangular room and wants to verify that the 4-sided room is square (meaning each corner forms a right angle). What might the carpenter do to verify that each corner forms a right angle without measuring the angles? 7. Suppose a room is constructed in the shape of a rhombus so that one diagonal is 6 ft. long and the other is 8 ft. long. Find the perimeter of the rhombus. 2007, TESCCC Revised 10/01/07 page 33 of 50

34 Properties of Quadrilaterals (pg 6) 8. Use the information in the trapezoid below to find the value of x, the value of y, m T, m R,and m P. T (12x+60)º (5y)º R P (4x+40)º 80º A 9. Suppose the length of EI is 10 ft. Use the information in the kite below to find the perimeter of the kite. K 45º 45º E 60º I 30º T 10. Use the information in the trapezoid below to find HK, IJ, m KHI, m KJI and m HIJ. H I 6 3 K 60º J 2007, TESCCC Revised 10/01/07 page 34 of 50

35 Quadrilaterals and Coordinate (KEY) Part A Draw figure ABCD using the following ordered pairs: A(0, 0), B(3, 4), C(-1, 7), and D(-4, 3). Complete the table below. Length of the four sides: AB = 5 CD = 5 BC = 5 DA = 5 Length of the diagonals: AC = 5 2 BD = 5 2 Angle measures at each vertex: m DAB =90º m BCD =90º m ABC =90º m CDA =90º Length of the diagonal segments: AE = BE = EC = ED = Slope of the four sides: Slope of AB = 4/3 Slope of CD = 4/3 Slope of BC = -3/4 Slope of DA = -3/4 Slope of the diagonals: Slope of AC = -7/1 Slope of BD = 1/7 Point of intersection of the diagonals (Point E) (-.5, 3.5) Angle measures of angles formed by diagonals: m AEB = 90º m CED = 90º m BEC = 90º m DEA = 90º How do you know that figure ABCD is a square? It has 4 right angles and 4 congruent sides. 2007, TESCCC Revised 10/01/07 page 35 of 50

36 Quadrilaterals and Coordinate (pg 2) KEY Squares 1. Write some conjectures you have about properties of squares and how the data you collected supports those conjectures. Opposite reciprocal slopes of sides verify right angles of the square. Opposite reciprocal slopes of diagonals verify that the diagonals are perpendicular. Length of diagonal segments are half the length of the diagonals, therefore, the diagonals bisect each other. 2. Create a square on the coordinate grid below that satisfies the following two conditions: a. The origin is not a vertex. b. No side is parallel to a coordinate axis. See student samples 3. How do you know that this figure is a square? It has 4 right angles and 4 congruent sides. 2007, TESCCC Revised 10/01/07 page 36 of 50

37 Quadrilaterals and Coordinate (pg 3) KEY Part B Draw figure ABCD using the following ordered pairs: A(0, 0), B(6, 8), C(2, 11), and D(-4, 3). Complete the table below. Length of the four sides: AB =10 CD =10 BC = 5 DA = 5 Length of the diagonals: AC =5 5 BD = 5 5 Angle measures at each vertex: m DAB =90º m BCD =90º m ABC =90º m CDA =90º Length of the diagonal segments: AE = BE = EC = ED = Slope of the four sides: Slope of AB = 4/3 Slope of CD = 4/3 Slope of BC = -3/4 Slope of DA = -3/4 Slope of the diagonals: Slope of AC = 11/2 Slope of BD = 5/10 Point of intersection of the diagonals (Point E) (1, 5.5) Angle measures of angles formed by diagonals: (approx.) m AEB 127º m CED 127º m BEC 53º m DEA 53º How do you know that figure ABCD is a rectangle and not a square? It has 4 right angles but does not have 4 congruent sides. 2007, TESCCC Revised 10/01/07 page 37 of 50

38 Quadrilaterals and Coordinate (pg 4) KEY Rectangles 4. Write some conjectures you have about properties of rectangles and how the data you collected supports those conjectures. Opposite reciprocal slopes of sides verify right angles of the rectangle. The data shows that the lengths of the diagonals of a rectangle are equal. Length of diagonal segments are half the length of the diagonals, therefore, the diagonals bisect each other. 5. Create a rectangle on the coordinate grid below that satisfies the following three conditions: a. The origin is not a vertex. b. No side is parallel to a coordinate axis. c. The figure is not a square. See student samples 6. How do you know that this figure is a rectangle? The figure has 4 right angles. 2007, TESCCC Revised 10/01/07 page 38 of 50

39 Quadrilaterals and Coordinate (pg 5) KEY Part C Draw figure ABCD using the following ordered pairs: A(0, 0), B(5, 5), C(6, 12), and D(1, 7). Complete the table below. Length of the four sides: AB = 5 2 CD = 5 2 BC = 5 2 DA = 5 2 Length of the diagonals: AC = 6 5 BD = 2 5 Angle measures at each vertex approx. m DAB 36.9 m BCD 36.9 m ABC m CDA Length of the diagonal segments: AE =3 5 BE = 5 EC =3 5 ED = 5 Slope of the four sides: Slope of AB = 1/1 Slope of CD = 1/1 Slope of BC = 7/1 Slope of DA = 7/1 Slope of the diagonals: Slope of AC = 1/2 Slope of BD = -1/2 Point of intersection of the diagonals (Point E) (3, 6) Angle measures of angles formed by diagonals: m AEB = 90 m CED = 90 m BEC = 90 m DEA = 90 How do you know that figure ABCD is a rhombus and not a square? It has 4 congruent sides but does not have four right angles. 2007, TESCCC Revised 10/01/07 page 39 of 50

40 Quadrilaterals and Coordinate (pg 6) KEY Rhombi 7. Write some conjectures you have about properties of rhombi and how the data you collected supports those conjectures. The slopes of the diagonals are opposite reciprocals verifies that the diagonals are perpendicular. The lengths of the diagonal segments are half the length of the diagonals verifies that the diagonals bisect each other. 8. Create a rhombus on the coordinate grid below that satisfies the following three conditions: a. The origin is not a vertex. b. No side is parallel to a coordinate axis. c. The figure is not a square. See student samples 9. How do you know that this figure is a rhombus? The figure has four congruent sides. 2007, TESCCC Revised 10/01/07 page 40 of 50

41 Quadrilaterals and Coordinate Part A Draw figure ABCD using the following ordered pairs: A(0, 0), B(3, 4), C(-1, 7), and D(-4, 3). Complete the table below. Length of the four sides: AB = CD = BC = DA = Length of the diagonals: AC = BD = Angle measures at each vertex: m DAB = m BCD = m ABC = m CDA = Length of the diagonal segments: AE = BE = EC = ED = Slope of the four sides: Slope of AB = Slope of CD = Slope of BC = Slope of DA = Slope of the diagonals: Slope of AC = Slope of BD = Point of intersection of the diagonals (Point E) Angle measures of angles formed by diagonals: m AEB = m CED = m BEC = m DEA = How do you know that figure ABCD is a square? 2007, TESCCC Revised 10/01/07 page 41 of 50

42 Quadrilaterals and Coordinate (pg 2) Squares 1. Write some conjectures you have about properties of squares and how the data you collected supports those conjectures. 2. Create a square on the coordinate grid below that satisfies the following two conditions: a. The origin is not a vertex. b. No side is parallel to a coordinate axis. 3. How do you know that this figure is a square? 2007, TESCCC Revised 10/01/07 page 42 of 50

43 Quadrilaterals and Coordinate (pg 3) Part B Draw figure ABCD using the following ordered pairs: A(0, 0), B(6, 8), C(2, 11), and D(-4, 3). Complete the table below. Length of the four sides: AB = CD = BC = DA = Length of the diagonals: AC = BD = Angle measures at each vertex: m DAB = m BCD = m ABC = m CDA = Length of the diagonal segments: AE = BE = EC = ED = Slope of the four sides: Slope of AB = Slope of CD = Slope of BC = Slope of DA = Slope of the diagonals: Slope of AC = Slope of BD = Point of intersection of the diagonals (Point E) Angle measures of angles formed by diagonals: m AEB m CED m BEC m DEA How do you know that figure ABCD is a rectangle and not a square? 2007, TESCCC Revised 10/01/07 page 43 of 50

44 Quadrilaterals and Coordinate (pg 4) Rectangles 4. Write some conjectures you have about properties of rectangles and how the data you collected supports those conjectures. 5. Create a rectangle on the coordinate grid below that satisfies the following three conditions: c. The origin is not a vertex. d. No side is parallel to a coordinate axis. e. The figure is not a square. 6. How do you know that this figure is a rectangle? 2007, TESCCC Revised 10/01/07 page 44 of 50

45 Quadrilaterals and Coordinate (pg 5) Part C Draw figure ABCD using the following ordered pairs: A(0, 0), B(5, 5), C(6, 12), and D(1, 7). Complete the table below. Length of the four sides: AB = CD = BC = DA = Length of the diagonals: AC = BD = Angle measures at each vertex m DAB m BCD m ABC m CDA Length of the diagonal segments: AE = BE = EC = ED = Slope of the four sides: Slope of AB = Slope of CD = Slope of BC = Slope of DA = Slope of the diagonals: Slope of AC = Slope of BD = Point of intersection of the diagonals (Point E) Angle measures of angles formed by diagonals: m AEB = m CED = m BEC = m DEA = How do you know that figure ABCD is a rhombus and not a square? 2007, TESCCC Revised 10/01/07 page 45 of 50

46 Quadrilaterals and Coordinate (pg 6) Rhombi 7. Write some conjectures you have about properties of rhombi and how the data you collected supports those conjectures. 8. Create a rhombus on the coordinate grid below that satisfies the following three conditions: a. The origin is not a vertex. b. No side is parallel to a coordinate axis. c. The figure is not a square. 9. How do you know that this figure is a rhombus? 2007, TESCCC Revised 10/01/07 page 46 of 50

47 Trace the Ancestry KEY 1. Create a Family Tree of quadrilaterals based on their properties and parallel sides that shows how the various quadrilaterals are related. See diagram below Quadrilaterals Trapeziums Trapezoids Parallelograms Kites Isosceles Trapezoid Rectangle Rhombus Square 2007, TESCCC Revised 10/01/07 page 47 of 50

48 Trace the Ancestry (pg 2) KEY 2. For the quadrilateral represented by the ordered pairs A(0, -4), B(-4, 0), C(0, 4), D(4, 0): a. Graph the figure, labeling points. See student samples b. Name the quadrilateral. Square c. Find the length of each side. 4 2 d. Find the slope of each side. Slope AD is 1, Slope CD is -1, Slope BC is 1, Slope AB is -1. e. Identify all types of quadrilaterals it represents. Square, Rectangle, Rhombus, Parallelogram f. Justify your conclusions. Square- Opposite reciprocal slopes (-1 and 1) of sides verify right angles of the square; all side lengths are 4 2. Rectangle-The Square has 4 right angles. Rhombus-The Square has 4 congruent sides. Parallelogram-The Square has opposite sides parallel since consecutive angles are supplementary. 2007, TESCCC Revised 10/01/07 page 48 of 50

49 Trace the Ancestry 1. Create a Family Tree of quadrilaterals based on their properties and parallel sides that shows how the various quadrilaterals are related. 2007, TESCCC Revised 10/01/07 page 49 of 50

50 Trace the Ancestry (pg 2) 2. For the quadrilateral represented by the ordered pairs A(0, -4), B(-4, 0), C(0, 4), D(4, 0): a. Graph the figure, labeling points. b. Name the quadrilateral. c. Find the length of each side. d. Find the slope of each side. e. Identify all types of quadrilaterals it represents. f. Justify your conclusions. 2007, TESCCC Revised 10/01/07 page 50 of 50

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