Download Angle Relationships

Geometry
Teacher Key
Angle Relationships
Choose the angle that completes the angle relationship described in the drawing at
the top of the page.
Lines r and s are
parallel.
1 2
3 4
5 6
7 8
r
b
a
c
s
4 are alternate interior angles.
A. Angle 5 and angle _____
6
B. Angle 7 and angle _____ are vertical angles.
7 are corresponding angles.
C. Angle 3 and angle _____
b are complementary angles.
D. Angle a and angle _____
2 or 3 are adjacent supplementary angles.
E. Angle 4 and angle _____
8 are all congruent.
F. Angles1, 4, 5 and _____
2
G. Angle 3 and angle _____ are vertical angles.
4
H. Angles adjacent to angle 2 are angles 1 and _____.
7
I. Angle 2 and angle _____ are alternate exterior angles.
© 2003 CompassLearning, Inc.
Activity 67218
Geometry
Teacher Key
Angle Relationships
Read the definition below. Then write the angle relationship being described.
complementary
J. Angles whose measures total 90° are called ________________________
angles.
K. Two angles that lie in the same plane and share a common vertex and a common side,
adjacent
but no common interior points, are called ________________________ angles.
supplementary
L. Angles whose measures total 180° are called ________________________ angles.
M. Two non-adjacent angles formed by two intersecting lines are called
vertical
________________________ angles.
N. Angles that are in the same position relative to a line, lines, or a plane figure are called
corresponding
________________________ angles.
© 2003 CompassLearning, Inc.
Activity 67218
Geometry
Teacher Key
Connections
Think About It
Is this a true statement? Why or why not?
"Every pair of complementary angles is also adjacent." Explain.
SAMPLE
RESPONSE: Complementary angles can be adjacent in some figures, but
________________________________________________________________________
they
do not have to be. If you have two triangles, side by side, and one has an
________________________________________________________________________
angle
measuring 40° and the other triangle has an angle measuring 50°, those two
________________________________________________________________________
________________________________________________________________________
angles
are said to be complementary even though they are in two different figures.
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
Counting Diagonals
A triangle has 3 sides, but no diagonals. A rectangle has 4 sides and 2 diagonals. Use
drawings to complete the chart below. You will need to include all diagonals from each
vertex with no duplications. For example, in a pentagon, you can draw diagonals from only
3 of the vertices before you begin to retrace diagonals already drawn.
See if you can come up with a pattern in the number of diagonals. Use this pattern to
determine the number of diagonals in a 20-sided figure.
Number
of Sides
3
Number of
Diagonals
0
4
2
0+2
5
5
2+3
6
9
5+4
7
14
9+5
8
20
14 + 6
9
27
20 + 7
10
35
27 + 8
20
170
152 + 18
© 2003 CompassLearning, Inc.
Pattern
0
Activity 67218