Geometry Homework 6.1 Polygons Pages 325-327
Geometry pages 325-327 Polygons 6.1: 4-6, 11-20, 24, 27-30, 37, 42-43, 45 4) polygon 5) Not a polygon; one side is not a segment. 6) Not a polygon; two sides intersect only one other side. 11) 67 12) polygon 13) not a polygon 14) not a polygon 15) not a polygon 16) polygon 17) not a polygon 18) pentagon; convex 19) heptagon; concave 20) heptagon; concave 24) regular
Geometry pages 325-327 Polygons 6.1: 4-6, 11-20, 24, 27-30, 37, 42-43, 45 27) quadrilateral; regular 28) pentagon; none of these 29) triangle; regular 30) octagon; regular 37) 75 42) 20 43) 44 45) 4
Geometry Homework 6.2a Properties of Parallelograms (Part 1) Pages 333-334
Geometry pages 333-334 Parallelograms 6.2a: 7, 9, 11-12, 19, 26, 28, 32, 34, 38 7) LMJ; opp. s of a are. 9) Segment JM; opp. sides of a are. 11) KMJ; if 2 lines are cut by a transversal, then alt. int. s are. 12) 13; since opp. sides of a are. LM = QN = 13. 19) 29 ; opp. sides of a are, so m LMQ = m MQN since they are alternate interior s. 26) x = 14, y = 10
Geometry pages 333-334 Parallelograms 6.2a: 7, 9, 11-12, 19, 26, 28, 32, 34, 38 28) r = 6, s = 3.5 32) x = 2, y = 3 34) w = 1, z = 3 38) a. segment AB segment DC b. segment AD segment BC c. segment BD segment BD d. SSS e. corresponding f. segment AC
Geometry Homework 6.2b Properties of Parallelograms (Part 2) Pages 333-337
Geometry pages 333-337 Parallelograms 6.2b: 5, 13, 17, 27, 33, 35, 37, 39, 56, 60 5) KN ; diagonals of a bisect each other. 13) 7; since the diagonals of a bisect each other, LP = NP = 7. 17) 80 ; since consecutive s of a are supplementary, m NQL = 180 - m QLM = 80 27) a = 79, b = 101 33) u = 4, v = 18 35) b = 90, c = 80, d = 100
Geometry pages 333-337 Parallelograms 6.2b: 5, 13, 17, 27, 33, 35, 37, 39, 56, 60 37) r = 30, s = 40, t = 25 39) (Statement) 1. JKLM is a (Reason) 2. Opposite s of a are. (Statement) 3. 360 (Reason) 4. Substitution prop. of = (Statement) 5. m J; m K (Reason) (Reason) 6. Division 7. Definition of supplementary s
56) Geometry pages 333-337 Parallelograms 6.2b: 5, 13, 17, 27, 33, 35, 37, 39, 56, 60 Statement Reason 1. PQRS and TUVS are 1. Given 2. 1 2; 3 2 2. Opposite s of a are 3. 1 3 3. Transitive prop. of 60) B
Geometry Homework 6.3 Proving Quadrilaterals are Parallelograms Pages 342-344
Geometry pages 342-344 Quads. as 6.3: 2-4, 9-11, 14-19, 33 2) Yes; if opp. s of a quad. are, then it is a. 3) Yes; if an of a quad. is suppl. to both of its consec. s, then the quad. is a. 4) Yes; the quad. is a by def. of a. 9) Yes; if opp. s of a quad. are, then it is a. 10) Yes; if the diags. of a quad. bisect each other, then the quad. is a. 11) No; according to the Vertical s Thm., the given info is true for the diags. of any quad.
14) Yes; if opp. s of a quad. are and, then it is a. 15) Since corresp. parts of are, both pairs of opp. sides of ABCD are, so ABCD is a. 16) Since corresp. parts of are, AX CX, and BX DX. So ABCD is a. 17) 70 18) 60 19) 90 Geometry pages 342-344 Quads. as 6.3: 2-4, 9-11, 14-19, 33
33) Geometry pages 342-344 Quads. as 6.3: 2-4, 9-11, 14-19, 33 Q R Given: P is supplementary to Q and S. Prove: PQRS is a P S Statement 1) P is supplementary to Q and S 2) QR PS 3) QP RS 4) PQRS is a Reason 1) Given 2) Consecutive Interior 3) Consecutive Interior 4) definition of
Geometry Homework 6.4a Types of Parallelograms Pages 351-355
Geometry pages 351-355 6.4a: 3-8, 10-14, 33-38, 66 Types of Parallelograms 3) always 4) sometimes 5) sometimes 6) always 7) C, D 8) B, D 10) A, B, C, D 11) 45 2x = 90 2x 12) Always; all the s of a rectangle are right s, therefore. 13) Sometimes; if rectangle ABCD is also a rhombus (a square), then AB BC. 14) Always; the diagonals of a rectangle are. 33) 18 34) 50 35) 50 5x = 90 5x
Geometry pages 351-355 6.4a: 3-8, 10-14, 33-38, 66 Types of Parallelograms 36) 5 37) 1 38) 24 66) D
Geometry Homework 6.4b Types of Parallelograms Pages 351-355
Geometry pages 351-355 Types of Parallelograms 6.4b: 9, 18, 20-21, 46, 51, 67 9) B, D 18) rhombus, square 20) parallelogram, rectangle, rhombus, square 21) rhombus, square 46) proof (see following slides) 51) proof (see following slides) 67) B
Geometry pages 351-355 6.4b: 9, 18, 20-21, 46, 51, 67 Types of Parallelograms 46) Given: RSTU is a, SU RT Prove: STR UTR R S Statement 1) RSTU is a Reason 1) Given U T 2) SU RT 3) RSTU is a rhombus 4) STR UTR 2) Given 3) diags. of rhombus are 4) diags. of rhombus are bisectors
Geometry pages 351-355 Types of Parallelograms 6.4b: 9, 18, 20-21, 46, 51, 67 51) Given: PQRT is a rhombus. Prove: PR bisects TPQ and QRT. P Q Statement TQ bisects PTR and RQP. Reason T R 1) PQRT is a rhombus 2) PQ QR RT PT 3) PR PR, QT QT 4) PRQ PRT; PTQ RTQ 5) TPR QPR, TRP QRP, PTQ RTQ, PQT RQT 6) PR bisects TPQ & QRT. TQ bisects PTR and RQP. 1) Given 2) Quad. is a rhombus if and only if it has 4 sides. 3) Reflexive prop. of. 4) SSS post. 5) Corresp. parts of s are. 6) Def. of bisectors.
Geometry Homework 6.5a Trapezoids Pages 359-362
Geometry pages 359-362 Trapezoids 6.5a: 7-9, 16-18, 21-24, 51-52 7) 9 8) 5 9) 9.5 16) m K = m L = 136, m M = 44 17) m J = 102, m L = 48 18) m K = m L = 98, m J = 82 21) 12 22) 5 23) 10 24) 5 51) E 52) C
Geometry Homework 6.5b Kites Page 360
Geometry page 360 6.5b: 28-33, 47 Kites 28) AB = AD 3.61, BC = DC = 5 29) EF = GF 6.40, HE = HG 8.60 30) JK = JM 14.42, LK = LM 9.43 31) 95 32) 70 33) 90
Geometry page 360 6.5b: 28-33, 47 Kites 47) Given: ABCD is a kite with AB CB and AD CD. C Prove: A C, B D Draw diagonal BD. Since AB CB and AD CD, BCD BAD by the SSS Postulate. Corresponding s A and C are. A C COUNTEREXAMPLE: Assume temporarily that s B and D are. Then both pairs of opposite s are, resulting in ABCD being a and not a kite! B D B A D
Geometry Homework 6.6 Quadrilaterals Page 367-369
Geometry pages 367-369 Quadrilaterals 6.6: 2-6, 8-13, 16-18, 30-33, 45-47 d = diagonal p = both pairs o = opposite Property Rectangle Rhombus Square Kite Trapezoid 2) po X X X X 3) 1o X 4) d X X X 5) d X X 6) d bis X X X X Property Rectangle Rhombus Square Kite Trapezoid 8) po X X X X 9) 1o 10) all X X 11) po X X X X 12) 1o X 13)all X X
Geometry pages 367-369 Quadrilaterals 6.6: 2-6, 8-13, 16-18, 30-33, 45-47 16) trapezoid 17) square 18) kite 30) A and D or B and C; BC AD by Consec. Int s Converse, so if A D or B C, AB and DC are not and ABCD is a trapezoid. Since the base s are, ABCD is an isosceles trapezoid. 31) BE and DE; if the diagonals of a quad. bisect each other, the quad. is a
Geometry pages 367-369 Quadrilaterals 6.6: 2-6, 8-13, 16-18, 30-33, 45-47 32) AB and CD; if AB CD, then one pair of opposite sides are both and, and ABCD is a parallelogram. Since the diagonals are, ABCD is a rhombus. 33) AC and BD; because the diagonals of ABCD bisect each other, ABCD is a. If the diagonals of a are, then the is a rectangle.
Geometry pages 367-369 Quadrilaterals 6.6: 2-6, 8-13, 16-18, 30-33, 45-47 45) ; if the diagonals of a quad. bisect each other, the quad. is a. Since the diagonals are not, the is not a rhombus and since the diagonals are not, the is not a rectangle. 46) Rhombus; if the diagonals of a quad bisect each other, the quad is a. Because the diagonals are, the is a rhombus. Since AC BD, the is not a rectangle, so it is not a square. 47) Kite; AC BD and AC bisects BD, so you can use to prove that AB = AD and that CB = CD. BD does not bisect AC, so ABCD is not a. Opp sides are not, so ABCD is a kite.
Geometry Homework 6.7 Areas of Quadrilaterals Page 376-377
Geometry pages 376-377 Areas of Quadrilaterals 6.7: 9-13, 16-18, 20-28, 37-38 9) A = s 2 = 5 2 = 25 u 2 10)A = bh = (9)(4) = 36 u 2 11) A = ½d 1 d 2 = ½ (10)(8) = 40 u 2 12) A = ½d 1 d 2 = ½ (12)(12) = 72 u 2 13) A = ½h(b 1 + b 2 ) = ½ (6)(8 + 4) = 36 u 2 16) A = bh =(5)(9) = 45 u 2 17) A = bh =(15)(8) = 120 u 2 18) A = bh =(22)(21) = 462 u 2
Geometry pages 376-377 Areas of Quadrilaterals 6.7: 9-13, 16-18, 20-28, 37-38 20) A = ½(b 1 + b 2 )h = ½(6 + 10)(8) = 64 u 2 21) A = ½d 1 d 2 = ½ (38)(19) = 361 u 2 22) A = ½(b 1 + b 2 )h = ½(24 + 7)(24) = 372 u 2 23) A = bh = (16)(15) = 240 u 2 24) A = ½(b 1 + b 2 )h = ½(8 + 16)(14) = 168 u 2 25) A = ½d 1 d 2 = ½ (14)(10) = 70 u 2
Geometry pages 376-377 Areas of Quadrilaterals 6.7: 9-13, 16-18, 20-28, 37-38 26) bh = A 7x = 63 x = 9 cm 27) ½d 1 d 2 = A ½(8)(x) = 48 4x = 48 x = 12 ft 28) ½d 1 d 2 = A ½(2x)(16) = 48 16x = 48 x = 3 in 37) A = 2[½(b 1 + b 2 )h] = (16 + 30)12 = 552 in 2 38) A = bh + ½(b 1 + b 2 )h = (20)(16) + ½(9 + 20)(5) = 392.5 in 2
Geometry Homework Ch 7 Review Pages 446, 449-451
Geometry page 446: 1-3, 5-6 // page 449: 1-2, 7-13 Page 450-451: 1-2, 5, 10-12 1) Yes; the figure and its image appear to be. 2) No; the figure and its image are not. 3) Yes; the figure and its image appear to be. 5) 6)
Geometry page 446: 1-3, 5-6 // page 449: 1-2, 7-13 Page 450-451: 1-2, 5, 10-12 1) reflection in the y-axis 2) yes 7) reflection in line m 8) rotation about the intersection of lines m and n 9) 170 10) reflection in line m 11) T (or translation) 12) 10 units 13) glide reflection
Geometry page 446: 1-3, 5-6 // page 449: 1-2, 7-13 Page 450-451: 1-2, 5, 10-12 1) B 2) D 5) B 10) A, H, I, M, O, T, W, X, Y (vertical line of symmetry) 11) C, E, H, K, O, X (horizontal line of symmetry) 12) H, N, O, S, X, Z (rotational symmetry)