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page 1 Geometry – Workbook 4, Part 1 7. Worksheet G4-1 page 148 1. a) b) 4 sides 4 vertices 124° e) 104° f) 57° 23 sides Worksheet G4-4 page 153 4 sides 4 vertices d) 5 sides 5 vertices 1. d) e) 8 sides 8 vertices f) g) 3 sides 3 vertices h) 2. h) 8 sides 8 vertices i) 12 sides 12 vertices j) 10 sides 10 vertices k) 8 sides 8 vertices l) 8 sides 8 vertices a) 3. 2.- 4. 5. a) 3 sides b) 4 sides c) 5 sides d) 6 sides a) 3 b) 4 c) 4 d) 3 greater than b) more than 90° 1. a) N greater than c) less than 90° b) Y greater than d) more than 90° c) N less than e) more than 90° d) Y greater than f) less than 90° e) Y greater than g) more than 90° f) Y greater than h) less than 90° g) Y i) more than 90° h) N a) Less than 90° 2. Teacher to check. b) more than 90° 120° 3. c) less than 90° 30° Teacher to check – in all cases, the original lines will still be parallel. 4. b) d) more than 90° 150° a) less than 90° 60° b) less than 90° 40° c) more than 90° 120° d) d) less than 90° 30° e) e) more than 90° 140° f) more than 90° 110° g) less than 90° 45° h) more than 90° 135° 2. Teacher to check. a) No right angles d) e) f) Letters A, D Quadrilaterals B, C Shapes Letters Triangles A Quadrilaterals B, F,G Pentagons C, D Hexagons E, H Answers will vary. 7. 8. Answers will vary. Worksheet G4-5 page 156 c) 6. 5. less than 90° 1. 3. 4 curved sides 4 straight sides Teacher to check a) The angles in (b) and (d) are right angles. b) b) b) and d) are half angles 4. 2 curved sides 2 straight sides Triangles b) c) 6 sides 6 vertices Shapes 6. d) 1. c) m) 12 sides 12 vertices 5. 129° Worksheet G4-2 page 150 g) 4. c) 8. f) 3. Worksheet G4-3 page 152 3 sides 3 vertices e) 2. Answers will vary but, no, you can’t draw a polygon in which the number of sides does not equal the number of vertices. a) Answers will vary. b) B, E, H and I each have 4 right angles a) Answers will vary. b) K and R have both a right angle and an acute angle. A × × For use with JUMP Math’s Workbook 4 Part 1 (3rd Edition) ISBN 978-1-897120-42-2 4. In the angles provided, some of the lines are too short to be measured by a standard protractor. Please show your students how to use a ruler to extend the lines if necessary. × × × c) × f) × × × × × × g) × × 5. a) 1 pair b) 2 pairs c) 1 pair d) 2 pairs Answers may vary by a few degrees. a) 43° b) 30° Selected Answer Key – Workbook 4 1 page 2 Geometry – Workbook 4, Part 1 (continued) c) Worksheet G4-6 page 158 1. Property Shape Quadrilateral A, C, E, G, J, L d) NonB, D, F, H, I, Quadrilateral K 2. A, B, D, E, F, G b) A, E, G Property Shape c) C Equilateral B, G, H, J d) 4 sides e) 5 sides Not Equilateral A, C, D, E, F, I 5. H - 2 pairs 2. 3. 1 pair – trapezoid No right A, B, F, H, J c) 1 right I 2 pairs – parallelogram 2 right D, E 4 right C, G None 1 pair E C, G 2 pairs A, B, D, F, H Shape No right B, G, I, K 1 right J 2 right D, E, F 4 right A, C, H b) No parallel lines B, I, J 1 pair D, E 2 pairs C, F, G, H 3 pairs A Name Shape Triangle B, I Quadrilateral C, F, G, H Pentagon D, E, J Hexagon A Worksheet G4-8 page 161 1. Property Shape d) a) Property Property a) Shape 1 pair D, E, F, I 2 pairs A, C, G, H, K a) Each side of the triangle is 2.5 cm – should be circled b) Each side of the pentagon is 2 cm – should be circled 4 right angles top and bottom: 3 cm No parallel B, J lines 4. 6 - 7. Answers will vary. 8. a) all b) no c) no d) some 9. 11. Answers should include three of the following: quadrilateral – since it has 4 sides; parallelogram – since it has 2 pairs of parallel sides; rectangle – since it’s a parallelogram with 4 right angles; 12. a) rectangle b) parallelogram c) square d) rhombus For use with JUMP Math’s Workbook 4 Part 1 (3rd Edition) ISBN 978-1-897120-42-2 1. 2. a) 4, 6 b) 1, 2, 3, 5, 7 c) 4, 6 a) b) c) d) e) 3. b) Similarities: Both have 4 equal sides. Differences: A square contains 4 right angles. Answers will vary. Worksheet G4-10 page 164 1. 2. Similarities: Both have 2 pairs of parallel sides. Differences: A rhombus has 4 equal sides. 0 right angles a) Worksheet G4-9 page 163 rhombus – since it’s a parallelogram with 4 equal sides. all sides: 2 cm 2. Differences: A parallelogram has 2 pairs of parallel sides; a trapezoid has only 1 pair. 10. square or rhombus Shape – rectangle Shape – rhombus Similarities: Both have 4 sides; both have at least 1 pair of parallel sides. square or rectangle left and right: 2 cm b) c) Square: A parallelogram with 4 right angles and 4 equal sides Rhombus: A parallelogram with 4 equal sides c) G - 1 pair parallelogram b) Property F - 2 pairs square c) Shape Answers will vary. E - 0 pairs b) 2 pairs – rectangle g) D - 2 pairs rectangle a) b) C - 1 pair a) Rectangle: A parallelogram with 4 right angles 5. F (not equilateral) B - 2 pairs 4. a) f) A - 2 pairs 3. Each side of the rhombus is 1.5 cm – should be circled a) Worksheet G4-7 page 157 1. The two horizontal sides of the rectangle are 4 cm, and the two vertical sides are 1 cm – not equilateral b) congruent c) not congruent a) 2nd and 3rd b) 1st and 3rd c) 2nd and 3rd d) 1st and 2nd e) 1st and 3rd f) 1st and 2nd g) 1st and 3rd h) 2nd and 4th i) 1st and 3rd j) 2nd and 3rd 3. From left to right – A; B; shape not congruent to others; B; A; shape not congruent to others 4. Teacher to check. Selected Answer Key – Workbook 4 2 page 3 Geometry – Workbook 4, Part 1 (continued) Worksheet G4-11 page 165 1. Teacher to check. 2. Teacher to check. 3. Two A’s: Three B’s: 4. a) Worksheet G4-14 page 168 Worksheet G4-16 page 170 1. Teacher to check. 1. Example: Property a) b) 5. a) 1 line of symmetry: Two C’s: A 2. b) Answers may vary. Example: 2 lines of symmetry: Two D’s: B ** remaining shapes aren’t congruent with anything 4. Teacher to check. 5. a) b) 6. c) d) 4. no lines of symmetry Worksheet G4-13 page 167 b) 1. a) Answers will vary. b) Teacher to check lines of symmetry drawn on page. or Worksheet G4-12 page 166 1. Teacher to check. 2. Teacher to check. 3. a) b) √ 0 √ # of right angles 0 1 √ lines of symmetry? Y N √ # of lines of symmetry 1 0 √ equilateral? N N H, I, O and X all have two lines of symmetry. # vertices √ # edges √ # of parallel sides √ a) BATH b) BED c) MAD lines of symmetry? √ 1. A. 31, 31, 31 mm Equilateral # of lines of symmetry √ B. 37, 37, 52 mm Isosceles equilateral? 2. Answers will vary. C. 67, 40, 40 Isosceles 3. Students’ answers should include the following information: a) E. 25, 35, 35 Isosceles Teacher to check lines of symmetry drawn on page. T S P H # Edges 3 4 5 6 # L of S 3 4 5 6 If a polygon is regular, the number of edges it has will equal the number of lines of symmetry it has. For use with JUMP Math’s Workbook 4 Part 1 (3rd Edition) ISBN 978-1-897120-42-2 S? D? Worksheet G4-15 page 169 D. 50, 33, 68 Scalene Figure √ √ Parallelogram 0 b) 3 0 b) F. 29, 26, 26 Isosceles a) Teacher to check. 3 # of parallel sides Property Rhombus 0 7. # edges Answers will vary. Rectangle 2 2. √ a) Square 4 c) 3 # of right angles a) e) 3 b) 1 line of symmetry: No, because they are not the same shape F1 F2 S? D? # vertices 2 lines of symmetry: 3. Yes, because they are the same size and shape (colour doesn’t matter) a) b) Property Triangles Equilateral A, F Isosceles B, C, E Scalene 2. 3. D Teacher to check. a) Line width: 4.5 cm b) Line width: 4.4 cm Teacher to check. √ Property F1 F2 S? D? # vertices 5 5 √ # edges 5 5 √ # of parallel sides 0 1 # of right angles 0 0 √ lines of symmetry? Y Y √ # of lines of symmetry 5 1 √ equilateral? Y N √ ** but F1 has all straight sides and F2 includes a curved side! √ Selected Answer Key – Workbook 4 3 page 4 Geometry – Workbook 4, Part 1 (continued) 4. Worksheet G4-17 page 171 D & H have both properties: A F 4 √ # edges 3 4 √ # of parallel sides 0 2 √ Property 2: B, C, F, H # of right angles 0 4 √ C & H have both properties: lines of symmetry? Y Y # of lines of symmetry 1 4 equilateral? N E H G B Property 1: C, D, H A E B C H D F G √ Y D, E & H have both properties: 2. Answers will vary. 3. Students should include the following information in their descriptions: Property a) b) c) # vertices 4 3 6 # edges 4 3 6 # of parallel sides 1 0 3 # of right angles 0 1 0 lines of symmetry? Y N Y # of lines of symmetry 1 0 6 equilateral? N N Y Property Example answers: a) Because all four angles are right angles. b) All four sides are not always equal c) Only 2 sides are parallel – there are no 2 pairs of parallel sides. T - quadrilateral F - at least one right angle d) F - 6 vertices a) T - at least 2 pairs of parallel sides Parallelogram or rhombus 3. b) rectangle a) equilateral triangle c) trapezoid b) rhombus F1 F2 S? D? c) parallelogram 4 4 √ 1. 16 # edges 4 4 √ 2. A: Trapezoid # of parallel sides 1 1 √ # of right angles 2 0 √ lines of symmetry? N Y √ # of lines of symmetry 0 1 equilateral? N N B: Trapezoid C: Square √ D: Square E: Rectangle F: Rectangle 3. √ A: 4 names (square, rectangle, rhombus, parallelogram) B: 1 name (parallelogram) Worksheet G4-18 page 173 C: 2 names (rectangle, parallelogram) 1. D: 2 names (rhombus, parallelogram) A N Y N N B N N N Y C Y N Y N D Y Y Y Y E N Y N N 2. a) 7. Worksheet G4-19 page 174 # vertices At least one Right Angle? Property 2: D, E, G, H Teacher to check. T - no right angles F - 2 pairs of parallel sides √ b) Property 1: A, C, D, E, H 6. F - 5 sides T - no right angles Two pairs of Parallel Sides? c) c) √ Equilateral? b) F1 F2 S? D? 3 C F - 3 vertices T - equilateral Property # vertices D b) a) Quadrilateral? a) Shape 1. Student descriptions might include the following details: T - 4 vertices F - 2 pairs of parallel sides E: 1 name (trapezoid) 4. A & H. D & E and B & G; each pair is the same size and shape 5. a) Teacher to check. Example: b) Both shapes have two parallel sides T - 4 sides T - at least 2 right angles For use with JUMP Math’s Workbook 4 Part 1 (3rd Edition) ISBN 978-1-897120-42-2 Selected Answer Key – Workbook 4 4