Preparing for the Regents Examination Geometry, AK

15 a Use constructing a congruent angle
procedure.
b Use constructing a congruent angle
procedure.
c Construct a perpendicular bisector of a
segment to form a 90 angle. Then use
constructing a congruent angle procedure
to construct the sum.
d Use constructing an angle bisector
procedure.
e Use constructing an angle bisector
procedure for A. Then use constructing a
congruent angle procedure to construct
the sum.
16 Use construction of an equilateral triangle
procedure.
17 Use the construction of an equilateral
triangle procedure using the length of the
longer segment to construct the leg of the
isosceles triangle.
18 Using the compass, measure the radius and
construct a circle passing through the point
on the tangent line.
19 Use construction of a line tangent to a given
circle through a given point outside the circle
procedure.
20 Use procedures for constructing parallel lines
and perpendicular lines.
14-2 Concurrent Lines and
Points of Concurrency
(pages 407–408)
1 (4) obtuse
2 (3) at one of the vertices of the triangle
3 Check students’ constructions.
4 All at the same point
5 10
6 6 2 _
3
7 36
8 16.5
9 4.5
10 SP 4, SC 6
11 PB 15, PR 30
12 PA 15, QA 45
13 4 1 _
3
14 9
88 Chapter 14: Locus and Constructions
15 3 √ 3
16 QE 4, DE 6
17 a, b, c: all interior
18 a, b, c: all interior
19 a interior b on a side c exterior
20 a interior b at a vertex c exterior
21 Incenter: √ 3 , circumcenter: 2 √ 3
22 Incenter: 2 √ 3 , circumcenter: 4 √ 3
23 Incenter: 3 √ 3 , circumcenter: 6 √ 3
24 Incenter: 6, circumcenter: 12
25 Since AG GC, the base is the same and the
altitude is the same. Therefore, the area is the
same.
14-4 Six Fundamental Loci
and the Coordinate Plane
(pages 413–414)
1 (3) One concentric circle of radius 11 inches
2 (2) one line
3 (2) a point
4 (1) a circle of radius 4 with center at P
5 (4) a circle
Note: For exercises 6–17 check students’ sketches.
6 Circle with given point as center and
radius 3
7 Two parallel lines, one on each side of the
given line
8 One line parallel to and midway between the
given parallel lines
9 The perpendicular bisector of the segment
joining R and S
10 The perpendicular bisector of the segment
AB
11 A circle with radius 2.5 inches and the given
point as the center
12 The line that is the bisector of ABC
13 Two lines each the bisector of the vertical
angles
14 Two concentric circles with radii 5 and 9
15 One concentric circle midway between the
given circles
16 All the points in the interior of a circle with
the given point as the center and with a
radius 2 inches
17 A circle with the given point as the center
and a radius of 3 inches and all the points in
the exterior of that circle