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Geometry: 2-D Shapes – AP Book 5.2: Unit 7 AP Book G5-6 page 144 1. a) b) c) line segment 2 endpoints line 0 endpoints ray 1 endpoint 2. Teacher to check. 3. Teacher to check. 4. Teacher to check. 5. a) Left b) Left c) Left d) Left a) Same b) Not the same a) Left b) Left a) Greater b) Less c) Greater d) Greater 6. 7. 8. 7. 8. b) COPYRIGHT © 2013 JUMP MATH: NOT TO BE COPIED. CC EDITION 3. 1. 2. 3. 4. 3 sides 3 vertices a) Teacher to check. b) No b) 30 degrees c) 80 degrees b) more than 90 c) less than 90 d) more than 90 e) more than 90 f) less than 90 a) acute b) obtuse c) obtuse d) obtuse e) acute f) acute a) acute b) obtuse c) acute d) obtuse e) obtuse f) acute b) d) 5 sides 5 vertices acute 30 c) e) 6 sides 6 vertices obtuse 120 d) f) 8 sides 8 vertices obtuse 150 a) g) 8 sides 8 vertices acute 50 b) acute 30 5. 6. 11 sides 11 vertices c) C It is not a polygon because not all sides are line segments. b) 6 sides hexagon c) 3 sides triangle 5 sides pentagon Triangle: A, H Quadrilateral: B, G, I Pentagon: C, F Hexagon: D, E Other: J 5. Other 6. Teacher to check. Answer Keys for AP Book 5.2 No. 6 sides 6 vertices d) 4. b) c) BONUS 2. The number of sides is equal to the number of vertices. AP Book G5-9 page 151 7. 8. obtuse 115 d) acute 45 e) obtuse 153 Teacher to check. a) 90 35 55 b) 65 75 40 3. a) 108 b) 118 c) 120 4. Teacher to check. Teacher to check. 1. b) C, D, E c) A, C, D, F 2 7 1 3 3 b) Teacher to check. c) Teacher to check. d) No, because numbers cannot be both odd and even. 5. a) B C b) AP Book G5-10 page 153 F A D E BDF A E C 2. a) 6. B H C D b) A E C D B F G AP Book G5-11 page 155 3. a) B 1. E C D A F 2 b) B i) b) The baseline is not lined up with one arm of the angle. 58 A 7. 4. a) 130 b) 6. B b) 52 C Teacher to check. a) c) d) a) 5. obtuse 105 30 12 2. f) a) ii) 1. AP Book G5-8 page 148 AP Book G5-7 page 146 1. a) E A C D F 3. 4. 1 2 3 12 3 a) 30mm, 30 mm, 25 mm, 25 mm b) 20 mm, 21 mm, 21 mm, 27 mm a) 27 mm b) 20 mm c) 40 mm, 20 mm d) 22 mm a) 60 b) 90 c) 120 d) 95, 85 a) Teacher to check: A, B, G b) All angles equal: A, B, C, G 7 Equilateral: A, B, E, F, G DH c) E F A B G C T-19 Geometry: 2-D Shapes – AP Book 5.2: Unit 7 (continued) The overlap. e) Teacher to check. iv) 2. 3. 4. a) 90 52 b) 20 118 42 Teacher to check. b) acute c) right d) obtuse a) acute b) right c) acute d) obtuse F A D AP Book G5-12 page 157 1. EG 10. Teacher to check. a) Acute b) No, because all three angles of a triangle must add up to 180 so no two angles can be 90, nor can two angles be obtuse in the same triangle. 6. All three angles in an acute triangle are acute. 1. Teacher to check. a) 2. a) 8. isosceles b) equilateral b) Yes isosceles c) No d) scalene d) Yes a) i) scalene e) Yes ii) isosceles f) Yes iii) equilateral g) Yes h) No iv) isosceles b) i) right-angle 3. Teacher to check. ii) right-angle 4. Teacher to check. iii) acute 5. Teacher to check. iv) acute 9. 6. a) Teacher to check. b) Acute: A, D, F a) Right: C, G Obtuse: B, E Equilateral: D Isosceles: A, E, G Scalene: B, C, F c) i) 7. BCE G A F B iii) G A E Teacher to check drawings. a) Teacher to check. b) 90 c) Teacher to check, answers may vary. d) You can use right angles to draw parallel lines because they can check to see if a perpendicular line is crossing two parallel lines. CD F C 1. BF 2. a) a) parallelogram b) trapezoid trapezoid Trapezoids have only 1 pair of parallel sides, while parallelograms have 2 pairs. A quadrilateral cannot be both. ii) 108, 72 108, 72 iii) 90 90 90 90 Opposite angles of a parallelogram are equal. c) No. 4. P, P, T, T, P 5. a) Teacher to check. b) Circle i), ii), and v) c) Parallelograms L: 50 mm, 21 mm d) No, opposite angles are not equal. N: 32 mm, 23 mm b) b) K: 39 mm, 19 mm M: 25 mm, 35 mm Parallelograms: K, N Trapezoids: L, M Parallel sides equal: K, N Parallel sides not equal: L, M c) Parallelograms have equal length parallel sides, whereas trapezoids do not. d) i) 60 mm, 56 mm Other pair not parallel, a trapezoid 6. Teacher to check. AP Book G5-16 page 166 1. Teacher to check. Circle a, b, e. 2. a) Yes b) No 3. a) Right-angled b) They would not be right-angled triangles. c) Teacher to check. 4. Teacher to check. 5. b) ii) 40 mm, 40 mm Other pair parallel, parallelogram 5. E D Ron is incorrect because equal opposite side lengths does not mean that the sides are parallel. Also, the two sides that are parallel are not of equal length. It is a trapezoid. 1. a) C, G b) Teacher to check. c) None B, D 2 A 3 E, I 4 F 2 pairs d) 2. C, G, H 6. C F A c) C, F d) In the overlap section d) Diagonals of a rectangle are equal length and not perpendicular, which is not the same for other parallelograms a) Teacher to check; explanations may vary. Sample answer: All rectangles are also parallelograms because rectangles have two pairs of equal length, parallel sides. AP Book G5-15 page 164 Teacher to check. c) T-20 4. AP Book G5-14 page 162 ADE G Teacher to check drawings. i) 2 ii) 3 iii) 0 BONUS 2 b) D ii) b) No a) i) 120, 60 120, 60 A C G D F No c) 3. B E H AP Book G5-13 page 160 Teacher to check. b) parallelogram a) B C d) 5. 7. d) 3. 4 or 2 pairs e) 2 a) Yes Answer Keys for AP Book 5.2 COPYRIGHT © 2013 JUMP MATH: NOT TO BE COPIED. CC EDITION d) Geometry: 2-D Shapes – AP Book 5.2: Unit 7 (continued) Teacher to check; explanations may vary. Sample answer: The length of the other two sides are 6 cm and 15 cm because a rectangle is also a parallelogram, and they have equal length opposite sides. b) 7. 4. All angles in a quadrilateral add up to 360, so with three exact angles at 90, the fourth angle must also be 90. b) Teacher to check. Sample answer: Any parallelogram that has at least 2 right angles has to be a rectangle because of the number of degrees needed to add up to the required 360. BONUS They are perpendicular. a) Yes, as squares are two sets of parallel lines. b) Yes, as all four sides of a square are equal, as in a rhombus, and there are two sets of parallel lines. c) Yes, because angles in a quadrilateral add up to 360. All quadrilaterals with 4 equal angles will have 90, making it a rectangle. a) e) No, as a trapezoid does not have equal length sides, and only has one set of parallel lines. d) Overlap section e) No, as a polygon that is a rhombus and also rectangle must also be a square. b) COPYRIGHT © 2013 JUMP MATH: NOT TO BE COPIED. CC EDITION 2. 3. A B S? 3 3 Y 0 0 Y 0 1 N 3 2 N 2 0 N C D S? 4 4 Y 2 2 Y 4 0 N 2 2 Y 2 2 Y b) i) rhombus ii) no iii) rhombus a) Yes a) Teacher to check. Teacher to check. E F S? c) Different 6 5 N d) Teacher to check. 6 5 N e) Teacher to check. 3 0 N f) C a) Teacher to check. N b) B C D Teacher to check. a) No, because the sides are not of equal length. b) Teacher to check. 4. a) Square b) Rhombus c) Right-angled isosceles triangle AP Book G5-19 page 172 1. Teacher to check. 2. Teacher to check. 3. a) Quadrilateral Parallelogram b) Quadrilateral Parallelogram Rhombus c) Quadrilateral Parallelogram Rhombus Square Rectangle d) Quadrilateral Parallelogram Rectangle 4. Teacher to check. c) b) A E F b) 3. a) AP Book G5-17 page 168 1. a) AP Book G5-18 page 170 1. A: Parallelogram B: Rhombus C: Rectangle D: Square E: Trapezoid F: Trapezoid 2. 2 0 Y Y Y N Y N d) Teacher to check drawings. No. e) Teacher to check. BONUS c) B, C, D d) In the overlap section Answer Keys for AP Book 5.2 Teacher to check. BONUS Teacher to check. T-21