Download 1-7 - Ithaca Public Schools

Name_____________________________________ Class____________________________ Date________________
Lesson 1-7
Lesson Objectives
1 Use a compass and a straightedge to
construct congruent segments and
congruent angles
2 Use a compass and a straightedge to
bisect segments and angles
Basic Constructions
NAEP 2005 Strand: Geometry
Topic: Relationships Among Geometric Figures
Local Standards: ____________________________________
Vocabulary.
A straightedge is
A compass is
Perpendicular lines are
A perpendicular bisector of a segment is
An angle bisector is
A
D
C
B
J
K
N
L
Examples.
1 Constructing Congruent Segments Construct TW congruent
K
to KM.
Step 1 Draw a ray with endpoint T.
M
T
Step 2 Open the compass the length of KM.
Step 3 With the same compass setting, put the compass point
on point T. Draw an arc that intersects the ray. Label the
point of intersection W.
T
W
KM TW
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Geometry Lesson 1-7
Daily Notetaking Guide
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
All rights reserved.
Construction is
Name_____________________________________ Class____________________________ Date ________________
2 Constructing Congruent Angles Construct Y so that Y G.
Step 1 Draw a ray with endpoint Y.
Y
G
75
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Step 2 With the compass point on point G, draw an arc that intersects
both sides of G. Label the points of intersection E and F.
E
G
75
F
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Step 3 With the same compass setting, put the compass point on
point Y. Draw an arc that intersects the ray. Label the point
of intersection Z.
Y
Step 4 Open the compass to the length EF. Keeping the same
compass setting, put the compass point on Z. Draw an arc
that intersects with the arc you drew in Step 3. Label the
point of intersection X.
Y
)
Step 5 Draw YX to complete Y.
Y G
Daily Notetaking Guide
Z
X
Y
Z
Geometry Lesson 1-7
25
Name_____________________________________ Class____________________________ Date ________________
3 Constructing the Perpendicular Bisector
Given: AB.
* )
* )
Construct: XY so that XY AB at the midpoint M of AB.
A
B
A
B
A
B
Step 2 With the
compass setting, put the compass
point on point B and draw another long arc. Label the
points where the two arcs
as X and Y.
* )
Step 3 Draw XY . The point of intersection of AB and XY is M,
the
of AB.
* )
X
* )
A
XY AB at the midpoint of AB, so XY is the
of AB.
*
B
Y
)
4 Finding Angle Measures WR bisects AWB so that mAWR x
A
and mBWR 4x 48. Find mAWB.
R
x
W
m
m
Definition of
Substitute
for mAWR and
for
mBWR.
48
Subtract
x
from each side.
Divide each side by
mAWR Substitute
(
)
mBWR 4
mAWB m
mAWB 26
4x 48
B
Geometry Lesson 1-7
for x.
48 m
.
Postulate
Substitute
for mAWR and for mBWR.
Daily Notetaking Guide
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
* )
All rights reserved.
Step 1 Put the compass point on point A and draw a long arc.
Be sure that the opening is
than 12AB.
Name_____________________________________ Class____________________________ Date ________________
Quick Check.
1. Use a straightedge to draw XY. Then construct RS so that RS 2XY.
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2. a. Construct F with mF 2mB.
B
)
b. Explain how you can use your protractor to check that YP is the angle
bisector of XYZ.
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
X
P
Y
Z
3. Draw ST. Construct its perpendicular bisector.
)
4. If mJKN 50°, then find mNKL and mJKL. KN bisects JKL.
J
K
N
Daily Notetaking Guide
mNKL , mJKL L
Geometry Lesson 1-7
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