Geo_Book_Answers
Geo_Book_Answers
Geo_Book_Answers
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CHAPTER 4 REVIEW<br />
1. Their rigidity gives strength.<br />
2. The Triangle Sum Conjecture states that the<br />
sum of the measures of the angles in every triangle<br />
is 180°. Possible answers: It applies to all triangles;<br />
many other conjectures rely on it.<br />
3. The angle bisector of the vertex angle is also the<br />
median and the altitude.<br />
4. The distance between A and B is along the<br />
segment connecting them. The distance from A<br />
to C to B can’t be shorter than the distance from A<br />
to B. Therefore, AC CB AB. Points A, B, and C<br />
form a triangle. Therefore, the sum of the lengths<br />
of any two sides is greater than the length of the<br />
third side.<br />
5. SSS, SAS, ASA, or SAA<br />
6. In some cases, two different triangles can<br />
be constructed using the same two sides and<br />
non-included angle.<br />
7. cannot be determined<br />
8. ZAP by SAA<br />
9. OSU by SSS<br />
10. cannot be determined<br />
11. APR by SAS<br />
12. NGI by SAS<br />
13. cannot be determined<br />
14. DCE by SAA or ASA<br />
15. RBO or OBR by SAS<br />
16. AMD UMT by SAS, AD UT by<br />
CPCTC<br />
17. cannot be determined<br />
18. cannot be determined<br />
19. TRI ALS by SAA, TR AL by<br />
CPCTC<br />
20. SVE NIK by SSS, EL KV by<br />
overlapping segments property<br />
21. cannot be determined<br />
22. cannot be determined<br />
23. LAZ IAR by ASA, LRI IZL by<br />
ASA, and LRD IZD by ASA<br />
24. yes. PTS TPO by ASA or SAA<br />
25. ANG is isosceles, so A G. However,<br />
the sum of mA mN mG 188°. The<br />
measures of the three angles of a triangle must sum<br />
to 180°.<br />
26. ROW NOG by ASA, implying that<br />
OW OG . However, the two segments shown are<br />
not equal in measure.<br />
27. a g e d b f c. Thus, c is the<br />
longest segment, and a and g are the shortest.<br />
28. x 20°<br />
29. Yes. TRE SAE by SAA, so sides are<br />
congruent by CPCTC.<br />
30. Yes. FRM RFA by SAA. RFM <br />
FRA by CPCTC. Because base angles are<br />
congruent, FRD is isosceles.<br />
31. x 48°<br />
32. The legs form two triangles that are congruent<br />
by SAS. Because alternate interior angles are<br />
congruent by CPCTC, the seat must be parallel to<br />
the floor.<br />
33. Construct P and A to be adjacent. The<br />
angle that forms a linear pair with the conjunction<br />
of P and A is L. Construct A. Mark off the<br />
length AL on one ray. Construct L. Extend the<br />
unconnected sides of the angles until they meet.<br />
Label the point of intersection P.<br />
P<br />
A y L<br />
34. Construct P. Mark off the length PB on one<br />
ray. From point B, mark off the two segments that<br />
intersect the other ray of P at distance x.<br />
S 1<br />
A<br />
L P<br />
P z<br />
B<br />
x<br />
S 2<br />
x<br />
ANSWERS TO EXERCISES 59<br />
<strong>Answers</strong> to Exercises
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