DO NOW
Sketch each figure.
1) CD
2) GH
3) AB
4) Line m
5) Acute ABC
6) XY II ST
Basic Constructions
Geometry
Week 3 of 9
Unit 1: Logic & Reasoning
9/9 & 9/10
Standards & Objective
Standard 16.0
Students perform basic constructions with a straightedge and
compass, such as angle bisectors and perpendicular bisectors.
Objective:
• Use a compass and a straightedge to construct congruent
segments and congruent angles
• Use a compass and a straightedge to bisect segments and
angles
Example: Constructing Congruent Segments
Construct a segment congruent
to a given segment
Given: AB
Construct: CD so that CD = AB
Step 1: Draw a ray with
endpoint C
Step 2: Open the compass to
the length of AB
Step 3: With the same compass
setting, put the compass
point on point C. Draw an
arc that intersects the ray.
Label the point of
intersection D.
Practice: Constructing Congruent Segments
1. Construct XY
congruent to AB.
2. Construct VW so that
VW = 2AB
A●
●B
2 inches
Example: Constructing Congruent Angles
Construct an angle congruent to a
given angle.
Given:
A
Construct: S so that S = A
Step 1: Draw a ray with endpoint S
Step 2: With the compass point on
point A, draw an arc that intersects
the sides of A. Label the points of
intersection B and C.
Step 3: With the same compass
setting, put the compass point on
point S. Draw an arc and label its
point of intersection with the ray as
R.
Step 4: Open the compass to the
length BC. Keeping the same
compass setting, put the compass
point on R. Draw an arc to locate
point T.
Step 5: Draw ST
Practice: Constructing Congruent Angles
Construct D so that D = C
C
Constructing the Perpendicular Bisector
Construct the perpendicular bisector of
a segment.
Given: AB
Construct: XY so that XY AB at the
midpoint M of AB
Step 1: Put the compass point on point
A and draw a long arc as shown. Be
sure the opening is greater than ⅟2
AB.
Step 2: With the same compass
setting, put the compass point on
point B and draw another long arc.
Label the points where the two arcs
intersect as X and Y.
Step 3: Draw XY. The point of
intersection of AB and XY is M,
the midpoint of AB.
XY AB at the midpoint of AB, so that
XY is the perpendicular bisector of
AB.
Draw ST. Construct its perpendicular
bisector.
Practice: Constructing the Perpendicular
Bisector
Construct the perpendicular
bisector of AB
●
A
●
B
Finding Angle Measures
Angle Bisector: a ray that divides an
angle into two congruent angles.
KN bisects JKL so that m JKN = 5x25 and m NKL = 3x+5. Solve for x
and find m JKN.
m JKN = m NKL
5x – 25 = 3x + 5
5x = 3x + 30
2x = 30
X = 15
m JKN = 5x – 25 = 5(15) – 25 = 50
m JKN = 50
Definition of Angle Bisector
Substitute
Add 25 to each side
Subtract 3x from each side
Divide each side by 2
Substitute 15 for x
Practice: Finding Angle Measures
GH bisects FGI.
a) Solve for x
b) Find m HGI
c) Find m FGI
F
H
(4x – 14)
G
I
Constructing the Angle Bisector
Construct the bisector of an angle
Given: A
Construct: AX, the bisector of A
Step 1: Put the compass point on
vertex A. Draw an arc that
intersects the sides of A. Label
the points of intersection B and C.
Step 2: Put the compass point on
point C and draw an arc. With
the same compass setting, draw
an arc using point B. Be sure the
arcs intersect. Label the point
where the two arcs intersect as
X.
Step 3: Draw AX.
AX is the bisector of CAB.