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page 1 Geometry 1 – AP Book 4.1 AP Book G4-1 page 148 6. 1. 7. a) 4 sides 4 vertices b) 3 sides 3 vertices c) 4 sides 4 vertices d) 5 sides 5 vertices e) 6 sides 6 vertices f) g) 8. 2. 4. × × AP Book G4-3 page 152 Answers may vary by a few degrees. AP Book G4-2 page 150 2. Teacher to check a) 3. Teacher to check b) 30° 1. 4. Teacher to check c) 129° 3 sides 3 vertices 8 sides 8 vertices less than b) greater than d) 124° c) greater than 104° d) greater than AP Book G4-4 page 153 e) f) 57° e) less than 1. f) greater than b) greater than 90° g) greater than c) less than 90° h) greater than d) greater than 90° AP Book G4-5 page 156 e) greater than 90° 1. 2. The angles in (b) and (d) are right angles. 3. Teacher to check. k) 8 sides 8 vertices 4. l) 8 sides 8 vertices 5. a) 2. 12 sides 12 vertices 2 curved sides 2 straight sides b) b) 4 sides c) 5 sides d) 6 sides a) 3 b) 4 c) 4 d) 3 a) d) 3. Triangles A, D Shapes Letters Triangles A Quadrilaterals B, F,G Pentagons C, D Hexagons E, H 6. 7. Answers will vary. a) N less than 90° b) Y greater than 90° c) N h) less than 90° d) Y i) greater than 90° e) Y a) less than 90° 60° f) Y g) Y b) greater than 90° 120° h) N c) less than 90° 30° d) greater than 90° 150° a) less than 90° 60° b) less than 90° 40° c) greater than 90° 120° d) less than 90° 30° e) greater than 90° 140° greater than 90° 110° f) Letters 5. g) e) Shapes less than 90° f) No right angles c) 4 curved sides 4 straight sides 3 sides 43° a) 10 sides 10 vertices a) 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. b) and d) are half right angles j) a) 4. 1. 8 sides 8 vertices Quadrilaterals B, C 5. 23 sides 12 sides 12 vertices b) 3. Answers will vary but, no, you can’t draw a polygon in which the number of sides does not equal the number of vertices. i) m) A 8. b) Answers will vary BONUS: h) a) Answers will vary. a) Answers will vary. f) b) B, E, H and I each have 4 right angles g) a) Answers will vary. less than 90° 45° b) K and R have both a right angle and an acute angle. h) greater than 90° 135° BONUS: Answers will vary 2. Teacher to check. 3. Teacher to check – in all cases, the original lines will still be parallel. 4. b) × × × c) × d) e) × × × × Answer Key for AP Book 4.1 page 2 Geometry 1 – AP Book 4.1 (continued) f) b) × × × 5. a) 1 pair b) 2 pairs c) 1 pair d) 2 pairs 4. AP Book G4-6 page 158 1. Property a) A, B, D, E, F, G 5. b) A, E, G a) c) A, C, G, H, K left and right: 2 cm a) Each side of the pentagon is 2 cm – should be circled c) The two horizontal sides of the rectangle are 4 cm, and the two vertical sides are 1 cm – not equilateral b) 3. 4. Equilateral B, G, H, J d) 4 sides e) 5 sides Not Equilateral A, C, D, E, F, I f) F (not equilateral) g) Answers will vary. Property A, B, F, H, J AP Book G4-7 page 159 1 right I 2 right 1. 4 right a) b) parallelogram c) square d) rhombus a) 4 right angles; rectangle b) 4 right angles; square c) 0 right angles parallelogram Rhombus: A parallelogram with 4 equal sides 5. a) 2 pairs – rectangle D, E b) 1 pair – trapezoid C, G c) 2 pairs – parallelogram Property Shape 6 No parallel lines B, I, J 7. Answers will vary. E - 0 pairs 8. a) F - 2 pairs 1 pair D, E b) no G - 1 pair 2 pairs C, F, G, H c) no 3 pairs A d) some C - 1 pair c) D - 2 pairs H - 2 pairs None 1 pair E C, G A, B, D, F, H 3. a) 9. 2 pairs d) Shape 10. square or rhombus 11. Answers should include three of the following: Pentagon D, E, J No right B, G, I, K Hexagon A 1 right J 2 right D, E, F 4 right A, C, H Differences: A parallelogram has 2 pairs of parallel sides; a trapezoid has only 1 pair. AP Book G4-9 page 163 1. 2. a) 4, 6 b) 1, 2, 3, 5, 7 c) 4, 6 a) b) c) d) e) square or rectangle B, I Quadrilateral C, F, G, H Similarities: Both have 4 sides; both have at least 1 pair of parallel sides. all Triangle Shape c) Answers will vary. Name Property Similarities: Both have 4 equal sides. Differences: A square contains 4 right angles. Square: A parallelogram with 4 right angles and 4 equal sides B - 2 pairs 2. rectangle Rectangle: A parallelogram with 4 right angles Shape No right b) Shape – rhombus 2. Similarities: Both have 2 pairs of parallel sides. Differences: A rhombus has 4 equal sides. 0 right angles all sides: 2 cm Each side of the rhombus is 1.5 cm – should be circled C 12. a) Shape – rectangle Each side of the triangle is 2.5 cm – should be circled b) rhombus – since it’s a parallelogram with 4 equal sides. 4 right angles 2 pairs Shape A - 2 pairs a) top and bottom: 3 cm Property b) 1. D, E, F, I d) NonB, D, F, H, I, Quadrilateral K AP Book G4-8 page 161 1 pair Shape Quadrilateral A, C, E, G, J, L 2. Shape No parallel B, J lines × g) Property 3. Answers will vary. quadrilateral – since it has 4 sides; AP Book G4-10 page 164 parallelogram – since it has 2 pairs of parallel sides; 1. rectangle – since it’s a parallelogram with 4 right angles; 2. a) not congruent b) congruent c) not congruent a) 2 and 3 b) 1 and 3 nd st rd rd Answer Key for AP Book 4.1 page 3 Geometry 1 – AP Book 4.1 (continued) c) 3. 4. nd rd st nd Rectangle 2 st rd Rhombus 0 st nd st rd 2 and 3 d) 1 and 2 e) 1 and 3 f) 1 and 2 g) 1 and 3 h) 2 and 4 nd th st rd i) 1 and 3 j) 2 and 3 nd rd From left to right – A; B; shape not congruent to others; B; A; shape not congruent to others Square 4 c) Teacher to check. 2. Teacher to check. Teacher to check. 3. Two A’s: Figure T S P H 1. Teacher to check. # Edges 3 4 5 6 2. Teacher to check. # L of S 3 4 5 6 3. a) b) b) If a polygon is regular, the number of edges it has will equal the number of lines of symmetry it has. 4. AP Book G4-14 page 168 a) 1. a) a) Two D’s: 6. b) Example: 2 lines of symmetry: B Yes, because they are the same size and shape (colour doesn’t matter) c) 2 lines of symmetry 3. No, because they are not the same shape d) a) b) e) Answers will vary. H, I, O and X all have two lines of symmetry. a) BATH b) BED c) MAD Midpoint – 2.25cm b) Line width: 4.4 cm Midpoint – 2.2 cm Teacher to check. a) a) Answers will vary. b) Teacher to check lines of symmetry drawn on page. F1 F2 S? D? # vertices 3 3 √ # edges 3 3 √ # of parallel sides 0 0 √ # of right angles 0 1 √ lines of symmetry? Y N √ # of lines of symmetry 1 0 √ equilateral? N N Property S? D? # vertices √ # edges √ # of parallel sides √ √ AP Book G4-15 page 169 lines of symmetry? √ 1. # of lines of symmetry √ a) A. 31, 31, 31 mm Equilateral B. 37, 37, 52 mm Isosceles √ b) # of right angles no lines of symmetry AP Book G4-13 page 167 1. a) b) 1 line of symmetry: 4. or Line width: 4.5 cm 1. Answers may vary. D Teacher to check. a) Teacher to check. A 2. ** remaining shapes aren’t congruent with anything b) 2. Example: Two C’s: a) Scalene AP Book G4-16 page 170 1 line of symmetry: Triangles Isosceles B, C, E, F Property 5. 5. Property Equilateral A 3. Three B’s: Teacher to check. b) a) b) 4. F. 29, 26, 26 Isosceles Teacher to check lines of symmetry drawn on page. AP Book G4-12 page 166 AP Book G4-11 page 165 2. E. 25, 35, 35 Isosceles Parallelogram 0 7. Teacher to check. 1. D. 50, 33, 68 Scalene equilateral? 2. √ Answers will vary. C. 67, 40, 40 Isosceles Answer Key for AP Book 4.1 page 4 Geometry 1 – AP Book 4.1 (continued) F1 F2 S? D? Property a) b) c) # vertices 5 5 √ # vertices 4 3 6 # edges 5 5 √ # 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 ** but F1 has all straight sides and F2 includes a curved side! # of parallel sides 0 1 √ # of right angles 0 0 √ lines of symmetry? Y Y √ # of lines of symmetry 5 1 √ equilateral? Y N √ a) A F C D H E G B b) Property 1: C, D, H Property 2: B, C, F, H C & H have both properties: A N Y N N B N N N Y C Y N Y N D Y Y Y Y 2. N a) 4 b) b) F - 3 vertices 6. Both shapes have two parallel sides Teacher to check. All four sides are not always equal c) Only 2 sides are parallel – there are no 2 pairs of parallel sides. # of parallel sides 0 2 √ # of right angles 0 4 lines of symmetry? Y Y # of lines of symmetry 1 4 √ equilateral? N Y √ T - equilateral c) √ T - quadrilateral F - 2 pairs of parallel sides F - at least one right angle √ d) F - 6 vertices T - no right angles a) T - at least 2 pairs of parallel sides Parallelogram or rhombus F1 F2 S? D? 3. b) rectangle a) equilateral triangle c) trapezoid rhombus parallelogram 4 √ 4 √ c) # of parallel sides 1 1 √ 2 0 Property 2: D, E, G, H # of right angles D, E & H have both properties: lines of symmetry? N Y √ # of lines of symmetry 0 1 √ equilateral? N N B T - 4 vertices b) √ 4 F N Because all four angles are right angles. 4 4 G Teacher to check. Example: a) 3 # edges D H E a) Example answers: # vertices C A 5. T - no right angles F Property 1: A, C, D, E, H A & H. D & E and B & G; each pair is the same size and shape F - 5 sides B G 4. T - at least 2 right angles b) C H E: 1 name (trapezoid) √ # edges Property Y D: 2 names (rhombus, parallelogram) T - 4 sides F1 F2 S? D? 3 Y C: 2 names (rectangle, parallelogram) F - 2 pairs of parallel sides b) E D c) A a) # vertices D & H have both properties: Y A: 4 names (square, rectangle, rhombus, parallelogram) B: 1 name (parallelogram) Student descriptions might include the following details: Property AP Book G4-17 page 171 1. 4. 1. E N 3. At least one Right Angle? Property AP Book G4-18 page 173 Two pairs of Parallel Sides? Students should include the following information in their descriptions: Equilateral? 3. Quadrilateral? Students’ answers should include the following information: Shape 3. √ 7. AP Book G4-19 page 174 1. 16 2. A: Trapezoid B: Trapezoid √ C: Square D: Square E: Rectangle F: Rectangle 2. Answers will vary. Answer Key for AP Book 4.1