Draw a conclusion based on the results of Exercise 9.

25. Prove the Extended Angle

Addition Property by using the Drawing, the Given, and the Prove that follow. Given: ⬔TSW with and Prove: m ⬔TSW = m ⬔TSU + m ⬔USV + m ⬔VSW

26. The Angle-Addition Postulate

can be generalized as follows: “The measure of an angle equals the sum of the measures of its parts.” State a general conclusion about m ⬔GHK based on the figure shown.

27. If there were no understood

restriction to lines in a plane in Theorem 1.6.4, the theorem would be false. Explain why the following statement is false: “In space, the perpendicular bisector of a line segment is unique.” SV SU

12. Given:

⬔1 ⬵ ⬔2; ⬔3 ⬵ ⬔4 ⬔s 2 and 3 are complementary Prove: ⬔s 1 and 4 are complementary

18. Does the relation “is in love with” have a reflexive

property consider one person? a symmetric property consider two people? a transitive property consider three people?

19. This textbook has used numerous symbols and

abbreviations. In this exercise, indicate what word is represented or abbreviated by each of the following: a ⊥ b ⬔s c supp. d rt. e m ⬔1

20. This textbook has used numerous symbols and

abbreviations. In this exercise, indicate what word is represented or abbreviated by each of the following: a post. b ´ c ⭋ d e pt.

21. This text book has used numerous symbols and

abbreviations. In this exercise, indicate what word is represented or abbreviated by each of the following: a adj. b comp. c d ⬵ e vert.

22. If there were no understood restriction to lines in a plane

in Theorem 1.6.3, the theorem would be false. Explain why the following statement is false: “In space, there is exactly one line perpendicular to a given line at any point on the line.”

23. Prove the Extended Segment Addition Property by using

the Drawing, the Given, and the Prove that follow. Given: M -N-P-Q on Prove: MN + NP + PQ = MQ MQ AB 1 2

3 4

PROOF Statements Reasons 1. ⬔1 ⬵ ⬔2 and 1. ? ⬔3 ⬵ ⬔4 2. ? and ? 2. If two ⬔s are ⬵, then their measures are equal 3. ⬔s 2 and 3 are 3. ? complementary 3 4. ? 4. The sum of the measures of complementary ⬔s is 90 2, 4 5. m ⬔1 + m ⬔4 = 90 5. ? 6. ? 6. If the sum of the measures of two angles is 90, then the angles are complementary

13. Does the relation “is perpendicular to” have a reflexive

property consider line ? a symmetric property consider lines and m? a transitive property consider lines , m, and n?

14. Does the relation “is greater than” have a reflexive

property consider real number a? a symmetric property consider real numbers a and b? a transitive property consider real numbers a, b, and c?

15. Does the relation “is complementary to” for angles have a

reflexive property consider one angle? a symmetric property consider two angles? a transitive property consider three angles?

16. Does the relation “is less than” for numbers have a

reflexive property consider one number? a symmetric property consider two numbers? a transitive property consider three numbers?

17. Does the relation “is a brother of ” have a reflexive

property consider one male? a symmetric property consider two males? a transitive property consider three males? M P N Q

24. The Segment-Addition Postulate can be generalized as

follows: “The length of a line segment equals the sum of the lengths of its parts.” State a general conclusion about AE based on the following figure. T U V W S K 4 N M L G H 3 2 1 A B C D E