Geometry Homework 6.1 Polygons. Pages

Transcription

1 Geometry Homework 6.1 Polygons Pages

2 Geometry pages 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

3 Geometry pages 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

4 Geometry Homework 6.2a Properties of Parallelograms (Part 1) Pages

5 Geometry pages 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 = ) 29 ; opp. sides of a are, so m LMQ = m MQN since they are alternate interior s. 26) x = 14, y = 10

6 Geometry pages Parallelograms 6.2a: 7, 9, 11-12, 19, 26, 28, 32, 34, 38 28) r = 6, s = ) 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

7 Geometry Homework 6.2b Properties of Parallelograms (Part 2) Pages

8 Geometry pages 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 = m QLM = 80 27) a = 79, b = ) u = 4, v = 18 35) b = 90, c = 80, d = 100

9 Geometry pages 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) (Reason) 4. Substitution prop. of = (Statement) 5. m J; m K (Reason) (Reason) 6. Division 7. Definition of supplementary s

10 56) Geometry pages Parallelograms 6.2b: 5, 13, 17, 27, 33, 35, 37, 39, 56, 60 Statement Reason 1. PQRS and TUVS are 1. Given ; Opposite s of a are Transitive prop. of 60) B

11 Geometry Homework 6.3 Proving Quadrilaterals are Parallelograms Pages

12 Geometry pages 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.

13 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 Quads. as 6.3: 2-4, 9-11, 14-19, 33

14 33) Geometry pages 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

15 Geometry Homework 6.4a Types of Parallelograms Pages

16 Geometry pages a: 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

17 Geometry pages a: 3-8, 10-14, 33-38, 66 Types of Parallelograms 36) 5 37) 1 38) 24 66) D

18 Geometry Homework 6.4b Types of Parallelograms Pages

19 Geometry pages 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

20 Geometry pages b: 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

21 Geometry pages 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.

22 Geometry Homework 6.5a Trapezoids Pages

23 Geometry pages Trapezoids 6.5a: 7-9, 16-18, 21-24, ) 9 8) 5 9) ) 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

24 Geometry Homework 6.5b Kites Page 360

25 Geometry page b: 28-33, 47 Kites 28) AB = AD 3.61, BC = DC = 5 29) EF = GF 6.40, HE = HG ) JK = JM 14.42, LK = LM ) 95 32) 70 33) 90

26 Geometry page b: 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

27 Geometry Homework 6.6 Quadrilaterals Page

28 Geometry pages Quadrilaterals 6.6: 2-6, 8-13, 16-18, 30-33, 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

29 Geometry pages Quadrilaterals 6.6: 2-6, 8-13, 16-18, 30-33, ) 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

30 Geometry pages Quadrilaterals 6.6: 2-6, 8-13, 16-18, 30-33, ) 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.

31 Geometry pages Quadrilaterals 6.6: 2-6, 8-13, 16-18, 30-33, ) ; 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.

32 Geometry Homework 6.7 Areas of Quadrilaterals Page

33 Geometry pages Areas of Quadrilaterals 6.7: 9-13, 16-18, 20-28, ) 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

34 Geometry pages Areas of Quadrilaterals 6.7: 9-13, 16-18, 20-28, ) 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

35 Geometry pages Areas of Quadrilaterals 6.7: 9-13, 16-18, 20-28, ) 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] = ( )12 = 552 in 2 38) A = bh + ½(b 1 + b 2 )h = (20)(16) + ½(9 + 20)(5) = in 2

36 Geometry Homework Ch 7 Review Pages 446,

37 Geometry page 446: 1-3, 5-6 // page 449: 1-2, 7-13 Page : 1-2, 5, ) 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)

38 Geometry page 446: 1-3, 5-6 // page 449: 1-2, 7-13 Page : 1-2, 5, ) reflection in the y-axis 2) yes 7) reflection in line m 8) rotation about the intersection of lines m and n 9) ) reflection in line m 11) T (or translation) 12) 10 units 13) glide reflection

39 Geometry page 446: 1-3, 5-6 // page 449: 1-2, 7-13 Page : 1-2, 5, ) 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)