1. Geometry/Trig 2Name: ____________________________________ Chapter 5 PracticeDate: ____________________________________ 1. Figure is a Parallelogram2. Figure is a Square 3. Figure is a Rectangle 4. Figure is a Rhombus 21 16 a b x° y° For each problem (1-4) a and b are segment lengths; x and y are angle measures. 6 b ay° x° 36° 104° a = _______ b = _______ x = _______ y = _______ a = _______ b = _______ x = _______ y = _______ 5. If TR = 2x and RN = 5x - 9,then x= __________ 6. If TA = 4x + 9 and RN = 9x + 6, then x= ________ 7. If TA = 16, then TN = __________ T R A N x + 7 5x - 2 2y - 7 y + 18 x = _______ y = _______ b a 14 x° y° 25° 6 a = _______ b = _______ x = _______ y = _______ 8. x° y° 32° a b 3.2 a = _______ b = _______ x = _______ y = _______

2. 1.2.3. A D C B ABCD is a rectangle AC = x 2 BD = x + 72 x = _____ y = _____ x = _____ y = _____ ABCD is a square D A B C ABCD is a rhombus m  DAB = 15y - 35 m  DCB = 20x m  ADC = 80 D A B C m  DAB = 4x + 4y m  ADC = 8x – 4y ABCD is an isosceles trapezoid EF is the median AB = 8x - 2 EF = 3x + 7 DC = 3x + 6 D C BAB CD A ABCD is a parallelogram m  A = 5x + 9 m  B = 7x + 3 D AB C x = _____ y = _____ x = _____ y = _____ 4.5.6. E F EF y Geometry/Trig 2Name: ____________________________________ Chapter 5 Practice – page 2Date: ___________________________ ABCD is a trapezoid; EF is the median AE = 5x - 7BF = y 2 AD = 6x + 2FC = -y + 6

3. Geometry/Trig 2Name: ____________________________________ Chapter 5 Practice – page 3Date: ___________________________ Complete the chart without looking at your notes. PropertyParallelogramRectangleRhombusSquare All angles are right angles Both Pairs of Opposite sides are parallel All sides are congruent Both Pairs of Opposite angles are congruent Diagonals bisect interior angles of quad. Diagonals are perpendicular Diagonals are congruent Diagonals bisect one another Both Pairs of Opposite sides are congruent True and False __________1. All quadrilaterals are parallelograms. __________ 2. All parallelograms are quadrilaterals. __________ 3. All squares are rhombi. __________ 4. All rectangles are parallelograms. __________ 5. If a parallelogram has  diagonals and four congruent sides it must be a square. __________ 6. If diagonals of a quadrilateral are congruent, then the quadrilateral is a parallelogram. __________ 7. An isosceles trapezoid has two congruent bases. __________ 8. If diagonals of a quadrilateral bisect one another, then the quadrilateral is a parallelogram. __________ 9. All trapezoids are parallelograms. __________ 10. All parallelograms are rectangles. __________ 11. If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. __________ 12. All trapezoids are quadrilaterals. __________ 13. If one pair of opposite sides in a quadrilateral are parallel, then the quadrilateral is a parallelogram. __________ 14. All rhombi are squares. __________ 15. The sum of the interior angles of a trapezoid is 360. __________ 16. A square has congruent diagonals. __________ 17. A trapezoid can have four congruent sides. __________ 18. The diagonals of a rhombus are always congruent. __________ 19. If one pair of opposite sides in a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram. __________ 20. All rectangles have perpendicular diagonals. __________21. Diagonals of a rhombus bisect one another. __________22. An isosceles trapezoid has congruent legs. __________23. A trapezoid can have no congruent sides. __________24. The legs of a trapezoid are parallel. __________25. If two lines have equal slopes, then the lines are perpendicular.

4. Geometry/Trig 2Name: ____________________________________ Chapter 5 Practice – page 4Date: ____________________________________ Complete the blank with the word always, sometimes or never. 1. A square is _________________ a rhombus. 2. The diagonals of a parallelogram ________________ bisect one another. 3. A parallelogram with four congruent sides is _________________ a rectangle. 4. The diagonals of a rhombus are __________________ congruent. 5. A rectangle _______________ has opposite sides that are congruent. 6. A parallelogram __________________ has perpendicular diagonals. 7. A rectangle is ___________________ a square. 8. A square is ____________________ a rectangle. 9. A parallelogram _____________________ has opposite congruent angles. 10. A rhombus is ____________________ a rectangle. 11. A rhombus ______________________ has perpendicular diagonals. 12. A trapezoid is _______________________ a parallelogram. 13. A rectangle _____________________ has congruent diagonals. 14. A square ____________________ has four congruent sides. 15. A parallelogram ________________________ congruent diagonals. 16. A parallelogram is ______________________ a square. 17. A rectangle __________________________ has perpendicular diagonals. 18. A rectangle is ____________________________ a rhombus. 19. A trapezoid ____________________ has two pairs of opposite parallel sides. 20. A square is ______________________ a rhombus. 21. A rhombus is _____________________ a square. 22. A rhombus _____________________ has four right angles. 23. A parallelogram with congruent diagonals and four right angles is _________________ a rectangle. 24. Opposite sides of a parallelogram are __________________ congruent. 25. The legs of a trapezoid are ______________________ congruent. 26. A rhombus __________________ has four congruent angles. 27. A parallelogram has interior angles that ____________________________ add up to 360˚. 28. A square is ______________________ a trapezoid. 29. The bases of a trapezoid are __________________________ parallel. 30. A trapezoid is _____________________ a rhombus. 31. A rhombus ____________________________ has congruent diagonals. 32. A square is __________________________ a parallelogram. 33. The legs of a trapezoid are __________________________ parallel. 34. The bases of a trapezoid are _____________________ congruent.

5. Geometry/Trig 2Name: ____________________________________ Chapter 5 Practice – page 5Date: ___________________________ Complete each proof. A B CF GH 1 2 3 Given: BGCF is a parallelogram; AC  GH Prove:  A   H Statements Reasons Given:  KQJ   LQM Prove: KMLJ is a parallelogram M LJ K Q

6. Geometry/Trig 2Name: ____________________________________ Chapter 5 Practice – page 6Date: ___________________________ Draw each figure and use markings to identify all properties. ParallelogramRectangle RhombusSquare Trapezoid Isosceles Trapezoid

7. Geometry/Trig 2Name: ____________________________________ Chapter 5 Practice – page 7Date: ___________________________ 1. MA  TH and MH  AT: ________________________________________________________________ 2. MA // TH and MA  TH: _______________________________________________________________ 3. TX  XM and AX  HX: ________________________________________________________________ 4. HM  AT and HT // MA: _______________________________________________________________ 5.  MAT   MHT and  HMA   HTA: ______________________________________________________ 6.  MXH   TXA and  HMA   HTA: ______________________________________________________ 7. X is the midpoint of MT and HA: _________________________________________________________ 8.  MHA   HAT and  THA   MAH: ______________________________________________________ 9. HA  MT: _________________________________________________________________________ 10.  MHA   HAT and HT // MA __________________________________________________________ TH AM X Classify each figure as specifically as you can based on the markings in the diagram. 1.2.3. 4.5.6. Determine whether the given information is enough to conclude that Quad. MATH is a parallelogram. If it is, write the method used.

8. Geometry/Trig 2Name: __________________________ Unit 5 Study GuideDate: ___________________________ Section 5-1 Definitions: Parallelogram Theorems: 5-1: Opposite sides of a parallelogram are congruent. 5-2: Opposite angles in a parallelogram are congruent. 5-3: Diagonals of a parallelogram bisect one another. Know How To: set up algebraic equations by applying properties of parallelograms. Suggested Exercises: p. 168 #1-14, p. 169 #1-10, p. 170 #19-28 Section 5-2 Five ways to prove that a quadrilateral is a parallelogram (You will have to list these on your test.) 1. If both pairs of opposite sides are parallel, then the quadrilateral is a parallelogram (definition of a parallelogram). 2. If both pairs of opposite sides are congruent, then the quadrilateral is a parallelogram. 3. If one pair of opposite sides are both congruent and parallel, then the quadrilateral is a parallelogram. 4. If both pairs of opposite angles are congruent, then the quadrilateral is a parallelogram. 5. If the diagonals bisect one another, then the quadrilateral is a parallelogram. Know How To: determine and prove that a quadrilateral is a parallelogram. Suggested Exercises: p. 173 #1-11, p. 174-5 # 1-10, 19-22 Section 5-3 Theorems: 5-8: If two lines are parallel, then all points on one line are equidistant from the other lines. 5-9: If three parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal. 5-10: A line that contains the midpoint of one side of a triangle and is parallel to another side passes through the midpoint of the third side. 5-11: The segment that joins the midpoints of two sides of a triangle 1. is parallel to the third side. 2. is half the length of the third side. Know How To: apply these theorem by setting up and solving algebraic equations. Suggested Exercises: p. 179 #2-6p. 180-1 #1-17 Section 5-4 Definitions: Rectangle, Rhombus, Square Properties of Special Parallelograms: Refer to property chart from 5.4 Exploration note pages. Know How To: Classify a give quadrilateral, apply properties of special quadrilaterals by setting up and solving algebraic equations. Suggested Exercises: p. 187 #1-16 Know How To: Determine whether a given quadrilateral is a trapezoid; determine whether a trapezoid is isosceles; calculate the length of the median of a trapezoid; apply theorem 5-19 by setting up and solving algebraic equations. Suggested Exercises: p. 192 C.E #1-11, p. 192-3 #1-11, 14-18 Section 5-5 Definitions: Trapezoid, Base, Leg, Isosceles Trapezoid, Median of a Trapezoid Theorems: 5-18: Base angles of an isosceles triangle are congruent. 5-19: The median of a trapezoid 1. is parallel to the bases. 2. has the length equal to the average of the base lengths. Other Suggested Exercises: p. 197-8 Chapter Review #1-8, 13-16, 19-22 p. 199 Chapter Test (not 10-11)

9. Geometry/Trig 2Name: ____________________________________ Chapter 5 Practice – page 6Date: ___________________________ A (-5, 7) B (0, 9) C (2, -3) D (7, -1) Fill in the chart below. Show all work. Plot the points on the coordinate plane. Classify Quadrilateral ABCD as specifically as possible: ____________________________ Explain: _______________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ LengthSlope AB AC BD CD