Geometry/Trig 2 Name: ____________________________________

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

2. Geometry/Trig 2 Name: ____________________________________ Chapter 5 Practice – page 2 Date: ___________________________ 1. 2. 3. A B A B A B D C D C D mÐDAB = 4x - 2 mÐADC = 8y + 18 ABCD is a square C ABCD is a rectangle AB = x – 11 AD = 4y – 64 CD = 4x – 71 BC = 2y - 22 ABCD is a rhombus mÐDAB = 15y - 35 mÐDCB = 20x mÐADC = 80 x = _____ y = _____ Perimeter: _____ x = _____ y = _____ x = _____ y = _____ 4. 5. 6. A B A B A B E F E F y D C D C ABCD is a parallelogram mÐA = 5x + 9 mÐB = 7x + 3 D ABCD is a trapezoid; EF is the median AE = 5x - 7 BF = y AD = 6x + 2 FC = -y + 6 C ABCD is an isosceles trapezoid EF is the median AB = 8x - 2 EF = 3x + 7 DC = 3x + 6 x = _____ y = _____ x = _____ y = _____ x = _____

3. Chapter 5 Practice – page 3 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. An isosceles trapezoid has two congruent bases. __________ 7. All trapezoids are parallelograms. __________ 8. All parallelograms are rectangles. __________ 9. All trapezoids are quadrilaterals. __________ 10. All rhombi are squares. __________ 11. The sum of the interior angles of a trapezoid is 360. __________ 12. A square has congruent diagonals. __________ 13. The diagonals of a rhombus are always congruent. __________ 14. All rectangles have perpendicular diagonals. __________ 15. Diagonals of a rhombus bisect one another. __________ 16. An isosceles trapezoid has congruent legs. __________ 17. The legs of a trapezoid are parallel. 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 rectangle _______________ has opposite sides that are congruent. 4. A parallelogram __________________ has perpendicular diagonals. 5. A rectangle is ___________________ a square. 6. A square is ____________________ a rectangle. 7. A parallelogram _____________________ has opposite congruent angles. 8. A rhombus ______________________ has perpendicular diagonals. 9. A trapezoid is _______________________ a parallelogram. 10. A square ____________________ has four congruent sides. 11. A parallelogram is ______________________ a square. 12. A trapezoid ____________________ has two pairs of opposite parallel sides. 13. A square is ______________________ a rhombus. 14. A parallelogram with congruent diagonals and four right angles is _________________ a rectangle. 15. Opposite sides of a parallelogram are __________________ congruent. 16. The legs of a trapezoid are ______________________ congruent. 17. A parallelogram has interior angles that ____________________________ add up to 360˚. 18. The bases of a trapezoid are __________________________ parallel. 19. A trapezoid is _____________________ a rhombus. 20. The legs of a trapezoid are __________________________ parallel.

4. Chapter 5 Practice – page 4 State if the figure is a parallelogram. If it is a parallelogram, state by what theorem or property. H T 1. MA @ TH and MH @ AT: ____________________________ 2. MA ll TH and MA @ TH: ___________________________ 3. TX @ XM and AX @ HX: ____________________________ 4. HM @ AT and HT ll MA: ___________________________ X M A 5. ÐMAT @ÐMHT and ÐHMA @ÐHTA: ______________________________________________________ 6. ÐMXH @ÐTXA and ÐHMA @ÐHTA: ______________________________________________________ 7. X is the midpoint of MT and HA: _________________________________________________________ 8. ÐMHA @ÐHAT and ÐTHA @ÐMAH: ______________________________________________________ 9. HA @ MT: _________________________________________________________________________ 10. ÐMHA @ÐHAT and HT ll MA __________________________________________________________ Classify each figure as specifically as you can based on the markings in the diagram. 1. 2. 3. 4. 5. 6. Complete the chart without looking at your notes.

5. Chapter 5 Practice – page 5 What’s wrong? Examine the problem below that a student completed incorrectly. Identify the error and explain why it is incorrect. Explain how you should solve the problem correctly. Find the value of x. (5 points) ________________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ 6x = 2(4x – 1) 6x = 8x-2 -2x =2 x = 1 x = _____ 6x 4x-1 Draw each figure and use markings to identify all properties. Parallelogram Rectangle Rhombus Square Trapezoid Isosceles Trapezoid

6. Chapter 5 Practice – page 6 Complete the proof. Please number your steps! Given: ABCD is a parallelogram Prove: ΔABC  ΔCDA B C 3 4 1 2 D A Statements Reasons