Geo_Book_Answers

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