Download Aim #18: How do we do constructions involving special segments of

CC Geometry H
Aim #18: How do we do constructions involving special segments of a triangle,
polygons, and circles?
All constructions are done with a compass and straightedge.
Leave all construction marks.
Do Now
1. Construct PT parallel to line m.
(Construct a line ll to a given line through a point not on the line.)
P
m
2. Construct the set of points equidistant from points A and B.
A
B
3. Construct and label altitude AD and altitude CE. Label F, the intersection of
AD and CE.
F is the ________________ of ΔABC.
A
C
B
Triangle Constructions
1. Construct centroid C, the intersection of the medians.
T
U
S
2. Construct incenter I, the intersection of the angle bisectors.
T
U
S
3. Construct circumcenter C, the intersection of the perpendicular bisectors.
T
S
U
3. Construct a triangle congruent to a given triangle using SSS.
Construct ΔABC ≅ ΔXYZ using SSS.
Z
Y
X
4. Construct a triangle congruent to a given triangle using ASA.
Construct ΔABC ≅ ΔXYZ using ASA.
Z
Y
X
5. Construct a triangle congruent to a given triangle using SAS.
Construct ΔABC ≅ ΔXYZ using SAS.
Z
X
Y
6. Inscribe a square in a circle.
T
7. Inscribe a regular hexagon in a circle.
T
8. Construct an equilateral triangle in a circle.
T
Construction Practice
1. Construct ΔGHI ≅ ΔDEF
D
E
F
2. Construct equilateral ΔXYZ circumscribed about circle O.
O
3. In the diagram below, radius OA is drawn in circle O. Using a compass and a
straightedge, construct a line tangent to circle O at point A.
A
O
CC Geometry H
HW # 18
Name __________________________
Date ________________
1. Construct equilateral ΔXYZ inscribed in circle R.
R
2. Construct square ABCD inscribed in circle S.
S
3. Construct a hexagon inscribed in circle U.
T
4. When inscribing a square in a circle, you are relying on which fact about squares?
(1) They contain four right angles.
(2) They have opposite angles congruent.
(3) The diagonals are congruent and perpendicular.
(4) The diagonals bisect the angles.
5. When constructing a regular hexagon inscribed in a circle, which of the following
statements is not true?
(1) The length of the radius of the circle becomes the length of each side of the
hexagon.
0
(2) The interior angles of the hexagon each contain 60 .
(3) A series of 6 congruent equilateral triangles can be formed in the interior of the
hexagon.
(4) The perimeter of the hexagon is equal in length to the length of three diameters
of the circle.
6. Construct circumcenter C, the
intersection of the perpendicular
bisectors of ΔLMN.
F
M
G
E
N
L
7. Construct orthocenter O, the
intersection of the altitudes
of ΔEFG.
Review
7. Write an equation of the line that is perpendicular to the line 3y + 4 = x and
that passes through the point (3,-3)?
8. The lengths of the sides of the triangle all measure 6.
Find the area of the triangle, in simplest radical form.
6
6
6
0
9. If AB with endpoints A(1,-2) and B(4,-1) is rotated 90 about point B, at what
point does A land?
10. In right ΔABC with right ≮C and altitude CD, AD = 6 and DB = 2.
Find CD, AC, and CB, in simplest radical form.