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Unit 2 Language Of Geometry
Day 15 Constructions Notes
Name: ______________________________
Date: ___________________ Hour: _____
(PH Lesson 1-5)
Constructions use a straight edge and a compass to draw geometric figures. A
straight-edge is anything that can be used to draw a straight line. A compass
is a tool used to draw circles, or parts of circles.
Construction #1: Construct Congruent Segments
Construct:
Step 1:
so that
Draw a ray with endpoint C.
Step 2: Open the compass to the length of
.
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.
Try This #1: Construct a segment congruent to ̅̅̅̅
𝐏𝐐. Label the new segment ̅̅̅̅
𝐑𝐒.
Try This #2: Construct segment ̅̅̅̅
𝐓𝐔 so that TU = 2PQ.
Construction #2: Constructing Congruent Angles.
Given:
A
Construct:
S so that
S
A
Step 1:
Step 2:
Draw a ray with endpoint S.
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:
Step 4:
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.
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
S
.
A
Try This #3: Construct
F congruent to
P.
Try This #4: Construct
G with m G = 2m P.
Perpendicular lines are two lines than intersect for form right angles. Symbol: ┴
A perpendicular bisector of a segment is a line, segment, or ray that is perpendicular to the
segment at its midpoint. It bisects the segment into two congruent segments.
Construction #3: Constructing a perpendicular bisector.
Given:
Construct:
so that
at the midpoint M of
.
Step 1:
Step 2:
Put the compass point on point A and
draw a long arc as shown. Be sure the
opening is greater than
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.
AB.
Step 3:
Draw
of
The point of intersection
and
is M, the midpoint of
at the midpoint of
, so
.
is the perpendicular bisector of
Try This #5: Construct the perpendicular bisector of ̅̅̅̅
𝐏𝐐.
.
An angle bisector is a ray that divides an angle into two congruent coplanar angles. Its endpoint
is at the vertex.
Construction #4: Constructing the angle bisector.
Given:
A
Construct:
, the bisector of
A
Step 1:
Step 2:
Put the compass point on
vertex A. Draw an arc that
intersects the sides of A.
Label the points of intersection B and C.
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
.
is the bisector of
CAB.
Try This #6: Construct the angle bisector of
⃗⃗⃗⃗⃗⃗⃗⃗ bisects
Example 1: 𝑊𝑅
B.
AWB. m AWR = x and m BWR = 4x – 48. Find m AWB.
Homework: Page 23 # 4 – 10, Page 24 # 15 – 18 and Pages 37 – 40 #9 – 12, 26, 37 – 39