Construction Regents Review
Show all construction marks.
1. Construct the perpendicular bisector XY of the line segment AB,
B
A
2. Construct equilateral triangle ABC using segment DE as a side length.
D
E
A
3. Construct and label bisector QS of
PQR
P
Q
R
4. Construct
XYZ equal in measure to
A
C
B
ABC.
5. Construct HEF which measure 30 0.
F
E
6. Construct a line perpendicular to the
given line through the given point P.
P
7. Construct a right angle with vertex P.
P
8. Construct a line parallel to the given line through the given point P.
P
9. Construct ABC whose measure is one-half the measure of UVW.
U
V
W
10. Construct a 450 angle at vertex S.
S
11. Below, dilate circle O by a scale factor r = 1/2 using a compass. The center of
dilation is the center of the circle.
O
12. Using your compass, dilate circle C with radius CA from center O with a scale
factor r = 2.
O
C
13. The larger circle is a dilation of the smaller circle. Find the center of dilation O.
14. Construct a square inscribed in Circle O.
o
26. How to construct an inscribed equilateral Triangle
Steps to create an inscribed equilateral triangle
1. Draw any point on the circle. 2. Measure the length of the radius. 3. Make 6 equal arcs with the compass open to the length of the radius. (What you have just created is 6 invisible equilateral triangles from point T)
(Each of the central angles and therefore the arcs are 60o)
4. Connect every other arc.
(This creates an equilateral triangle with the inscribed angles each measuring 60o because they are half of the 180o arc that they intercept)
o
60 60o
60o
60o
60o 60o
Alternate method to construct an inscribed equilateral Triangle
Steps to create an inscribed equilateral triangle
1. Draw any point on the circle. 2. Lightly draw the radius. 3. Construct the perpendicular bisector of the radius. (This creates one side of the equilateral triangle.) 4. Construct the remaining sides of the triangle using the side you just created.