Geo_Book_Answers
Geo_Book_Answers
Geo_Book_Answers
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1 OR CD<br />
?<br />
5 OC OD<br />
?<br />
All radii of<br />
a circle are<br />
congruent<br />
LESSON 6.3<br />
1. 65° 2. 30° 3. 70° 4. 50°<br />
5. 140°, 42° 6. 90°, 100° 7. 50° 8. 148°<br />
9. 44° 10. 142° 11. 120°, 60°<br />
12. 140°, 111° 13. 71°, 41° 14. 180°<br />
15. 75°<br />
16. The two inscribed angles intercept the same<br />
arc, so they should be congruent.<br />
17. BFE DFA (Vertical Angles Conjecture).<br />
BGD FHD (all right angles congruent).<br />
Therefore, B D (Third Angle Conjecture).<br />
mB 1<br />
2 mAC ,mD 1<br />
2 mEC ,AC EC <br />
18. Possible answer: Place the corner so that it is<br />
an inscribed angle. Trace the inscribed angle. Use<br />
the side of the paper to construct the hypotenuse<br />
of the right triangle (which is the diameter). Repeat<br />
the process. The place where the two diameters<br />
intersect is the center.<br />
19. possible answer:<br />
It works on acute and right triangles.<br />
20. The camera can be placed anywhere on the<br />
major arc (measuring 268°) of a circle such that the<br />
row of students is a chord intersecting the circle to<br />
form a minor arc measuring 92°. This illustrates<br />
the conjecture that inscribed angles that intercept<br />
the same arc are congruent (Inscribed Angles<br />
Intercepting Arcs Conjecture).<br />
21. two congruent externally tangent circles with<br />
half the diameter of the original circle<br />
24. (Lesson 6.3)<br />
Given<br />
<br />
6<br />
OCD is isosceles<br />
?<br />
2<br />
ORC and ORD<br />
are right angles<br />
Definition of<br />
perpendicular lines<br />
?<br />
Definition of<br />
isosceles triangle<br />
22. a 108°; b 72°; c 36°; d 108°;<br />
e 108°; f 72°; g 108°; h 90°; l 36°;<br />
m 18°; n 54°; p 36°<br />
23. (2, 1); Possible method: Plot the<br />
three points. Construct the midpoint and the<br />
perpendicular bisector of the segments connecting<br />
two different pairs of points. The center is the point<br />
of intersection of the two lines. To check, construct<br />
the circle through the three given points.<br />
24. See flowchart below.<br />
25. Start with an equilateral triangle whose vertices<br />
are the centers of the three congruent circles. Then<br />
locate the incenter/circumcenter/orthocenter/<br />
centroid (all the same point because the triangle is<br />
equilateral) to find the center of the larger circle. To<br />
find the radius, construct a segment from the<br />
incenter of the triangle through the vertex of the<br />
triangle to a point on the circle.<br />
26. mA 60°, mB 36°, mC 90°;<br />
60° 36° 90° 180°<br />
3 mORC 90<br />
mORD 90<br />
?<br />
7 C ?<br />
?<br />
Definition of<br />
right angle<br />
D<br />
7. Isosceles Triangle<br />
Conjecture<br />
4 mORC mORD<br />
(ORC ORD)<br />
?<br />
8 OCR ?<br />
?<br />
9 CR ?<br />
?<br />
10 OR bisects CD<br />
?<br />
Substitution<br />
property<br />
SAA<br />
DR<br />
CPCTC<br />
ODR<br />
Definition of bisect<br />
ANSWERS TO EXERCISES 77<br />
<strong>Answers</strong> to Exercises