Name:Date:

Review: 3.1, 3.2 & 3.5

1. Refer to the figure to the right to identify each of the following.

a. all planes that intersect plane STX b. all segments that intersect QU

c. all segments that are parallel to XY d. all segments that are skew to VW

2. a. Given: j II pIf 2 of the 6 anglesare chosen at random,what is the probabilitythey are alwayscongruent?

b. Given: j II p

Geometry Honors

12z)°mZl = (3x + 4ymZ6 = (x - 8y)°Solve for x in termsof y and 2.

c. Given:mZl = (3x + 4)°mZ4 = (2x + 40)°mZ5 = (x + 34)°Solve for x anddetermine if j II p.

3. If m||n , find 2.

m

4. What's wrong with this picture?

/56°< »*^

5. Find a, b, and c. 6a. mZl = (3x-4y)°mZ2 = (y - 10)°mZ3 = (x - y)°Find mZl.

= (3x2)0

Find mZl.

->->-

7. Name the relationship between Z2 and each of the givenangles. In each case, state which line is the transversal.

a. Z3

c. Z7

e. Zll

b. Z10

d. Z4

8. Find all angles that have the given Use diagram below 9. Determine which lines, if any, must be parallel,relationship with Z6 . for #8 4 9. jf any |jnes are para|lel, state the reason why.

a. Alternate Interior

b. Corresponding

c. Consecutive Interior

9112/6 10/12

3/7 /

Tl

a. Z1^Z3 b.

c. Z6suppZ7 d.

10. Which of the following statements is w/alwaystrue if two parallel lines m and n are cut bytransversal t?

a. Corresponding angles are congruent.b. Alternate interior angles are congruent.c. Exterior angles are congruent.d. Consecutive interior angles are supplementary

11. If two parallel lines are cut by a transversal,which angles could be complementary?

I. Alternate Interior ZsII. Consecutive Interior Zs

III. Corresponding Zs

a. I only b. II onlyc. I and III only d. II and III onlye. I, II, and III

For # 12 4 13, a || b. Find the value of x, mZl, and mZ2.12. 13.

^_ \130° . „

>b

14. Find the values of x and y. 15. If mZ4 = (3x-24)° and

find mZ2.

\ \1\2 3V4

16. If AAN || PO, is Z2 supp Z6 ? Why or why not?

Is Z4 supp Z6 ? Why or why not? M

17. Using what you know about parallel lines,transversals, and alternate interior angles,write an argument that the consecutiveinterior angles are supplementary. Referto the diagram for your argument.

1/3

18. Solve for a in terms of b and c.

19. Refer to the diagram to the right.a. If mZ3 = 5(x + 2)° and mZ7 = 3(x + 10)°, find mZ8.

b. If mZ3 = (2x + 6)° and mZ5 = (7x-15)°, find mZ2.

c. Is Z3 ̂ Z6 ? Explain.d. Is Z2 supp Z7 ? Explain.

e. Is ZlsuppZ6? Explain.

20. Find each angle measure, (a-i)

Write a two-column proof for each22. Given: Zl s Z3

Z2sZ4

Prove: a II b

c. ZDAE and ZADE are _with transversal

23. Given: m II nZ5sZ6

Prove: p II q

6\ 4\

>b \

75/6

a. ZBAb and ZADE are

b. ZACF and ZADF are

Z's between lines and

Z's between lines and

Z's between lines and

24. Given: ZABCsZ&BEZ3 supp Z4

Prove: AD II EC

ANSWERS:la. TUZ, SRW, STU, VWX, QUV, QVW

b. QR, QV, TU, UZ

c. ST

d. QU, RS, ST, SX, TU, TY,DZ

2a. £

b. x = y - 3z + 45c. x = 36, j is not parallel to p because mZ4 = 112° and mZ5 = 70° .'. consecutive interiors Zs are not supp

3. 113° 4. consecutive exterior angles are not supp 5. a = 45°, b = 135°, c = 45°

6a. 10° b. 3° or 12°

7a. consecutive interior Zs, I b. corresponding Zs , p c. alternate interior Zs, I d. corresponding Zs , I

e. alternate exterior Zs , p

8a. Z3 and Z9 b. Z8 and Z12 c. Z7 and Z10

9a. p || q, corresponding Zs ̂ b. none c. p || q, consecutive interior Zs supp d. 11| m, alternate interior Zs ̂

e. p || q, alternate exterior Zs =

10. c 11. c 12. x = 20, mzl = 50°, mZ2 = 130° 13. x = 24, mZl = 88°, mZ2 = 92° 14. x = 16, y = 40 15. 51°

16. Yes. Z2 and Z6 are supp because they are consecutive interior Zs between parallel lines MN and PO.No. Z4 and Z6 are also consecutive interior Zs but they are not between lines that are parallel.

17. Zl supp Z3 because of definition of linear pair. Zl = Z2 because if parallel, then alternate interior Zs =.By substitution, Z2 supp Z3.

18. a = -b - c + 270

19a. 120° b. 48° c. Yes. If ||, then alternate interior Zs are ̂ .

d. If ||, then alternate exterior Zs are =. However, unless they are right Zs , they are not supp.

e. Yes. If ||, then consecutive exterior Zs are supp. Therefore, Zl supp Z7. Vertical Zs are ̂ , so

Z7 £ Z6. By substitution, Zl supp Z6.

20. a = 152° b = 28° c = 152° d = 76° e = 90° f = 118° g = 62° h = 62° i = 152°

21a. alternate interior angles AB, DE, AD b. corresponding angles CF, DF, AD c. consecutive interior AE, DE, AD

22. 23. 24.

Statements1. ZlsZS2. Z2 = Z43. Z1-Z24. Z3sZ45. a II b

Reasons1. Given2. Given3. Vertical Zs =4. Transitive5. Ifaltext=,

then II.

Statements1. mlln2. Z4 = Z5

3. Z5-Z64. Z4 = Z65. p l lq

Reasons1. Given2. If II, then alt

int Zs =.3. Given4. Transitive5. If corr Zs =.

then II.

Statements1. ZABC = ZDBE2. Z2sZ23. ZABC - Z.2 = ZbBE - Z2

4. ZlsZS5. Z3 supp Z46. Zl supp Z4

7. AD II EC

Reasons1. Given2. Reflexive3. Subtraction4. Substitution5. Given6. Substitution

7. If cons int Zssupp, then II.