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Curriculum Information
SOL Reporting Category
Measurement and Geometry
Focus
Problem Solving
Virginia SOL 8.6
The student will
a. verify by measuring and describe
the relationships among vertical
angles, adjacent angles,
supplementary angles, and
complementary angles; and
b. measure angles of less than 360°.
Essential Knowledge and Skills
Key Vocabulary
Essential Questions and Understandings
Teacher Notes and Elaborations
The student will use problem solving,
mathematical communication,
mathematical reasoning, connections
and representations to:
 Measure and draw angles of less than
360° to the nearest degree, using
appropriate tools.
 Identify and describe the relationships
between angles formed by two
intersecting lines.
 Classify the types of angles formed by
two lines and a transversal.
 Identify and describe the relationship
between pairs of angles that are vertical.
 Identify and describe the relationship
between pairs of angles that are
alternate interior angles and same side
interior angles.
 Identify and describe the relationship
between pairs of angles that are
supplementary.
 Identify and describe the relationship
between pairs of angles that are
complementary.
 Identify and describe the relationship
between pairs of angles that are
adjacent.
 Use the relationships among
supplementary, complementary,
vertical, and adjacent angles to solve
practical problems.
 Solve practical problems by using the
relationship between pairs of angles
such as vertical angles, alternate interior
angles, same side interior angles,
complementary and supplementary
angles.
 Identify lines as parallel, intersecting,
or perpendicular.
Essential Questions and Understandings
 How are vertical, adjacent, complementary and supplementary angles related?
Adjacent angles are any two non-overlapping angles that share a common side and a
common vertex. Vertical angles will always be nonadjacent angles. Supplementary
and complementary angles may or may not be adjacent.
 What are the relationships between the angles formed when two parallel lines are cut by
a transversal?
When two parallel lines are cut by a transversal, several pairs of angles are formed.
Pairs of alternate interior angles, and vertical angles are congruent. Adjacent angles,
and same side (consecutive) interior angles are supplementary.
Teacher Notes and Elaborations
Lines that have one and only one point in common are known as intersecting lines. When
two lines intersect, four non-overlapping angles are formed.
Parallel lines are lines that are in the same plane and never intersect because they are
always the same distance apart. They have no points in common. The symbol || indicates
parallel lines.
Perpendicular lines are lines that intersect at right angles.
Two angles are congruent if they have the same measure.
A vertex is a common point to the two sides of an angle or a polygon.
When two lines intersect two types of angle pairs are formed: vertical angles and adjacent
supplementary angles. Adjacent angles are any two non-overlapping angles that share a
common side and a common vertex. Vertical angles are all nonadjacent angles formed by
two intersecting lines. Vertical angles are congruent and share a common vertex. The
adjacent angles are supplementary. Nonadjacent angles do not share a common side.
Complementary angles are any two angles such that the sum of their measures is 90°. When
complementary angles are adjacent, they form a right angle. Supplementary angles are any
two angles such that the sum of their measures is 180°. When supplementary angles are
adjacent, they form a straight angle. A straight angle is an angle whose measure is 180º.
A transversal is a line that intersects two or more coplanar lines in different points forming
eight angles. Interior angles lie between the two lines.
(continued)
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Updated: 8-29-16
Curriculum Information
SOL Reporting Category
Measurement and Geometry
Essential Knowledge and Skills
Key Vocabulary
Cognitive Level (Bloom’s Taxonomy, Revised)
Remember – Classify, Describe, Identify
Apply – Apply, Use, Solve, Measure
Analyze - Draw
Focus
Problem Solving
Virginia SOL 8.6
The student will
a. verify by measuring and describe
the relationships among vertical
angles, adjacent angles,
supplementary angles, and
complementary angles; and
b. measure angles of less than 360°.
Key Vocabulary
adjacent angles
alternate interior angles
complementary angles
congruent
intersecting lines
nonadjacent angles
parallel lines
perpendicular lines
protractor
reflex angles
same side interior angles
straight angle
supplementary angles
transversal
vertex
vertical angles
Essential Questions and Understandings
Teacher Notes and Elaborations
Teacher Notes and Elaborations (continued)
Alternate interior angles are on opposite sides of the transversal. Same side (consecutive)
interior angles are on the same side of the transversal. Exterior angles lie outside the two
lines. Alternate exterior angles are on opposite sides of the transversal.
If two parallel lines are cut by a transversal, then alternate interior angles are congruent. If
two parallel lines are cut by a transversal, then same side(consecutive) interior angles are
supplementary.
Given parallel lines and the transversal (t), students should identify, classify, and describe
angle relationships.
1
3
5
7
2
4
6
8
t
Examples:
1 and 2 is a pair of adjacent supplementary angles.
4 and 6 and 3 and 5 are pairs of same side interior supplementary
angles.
1 and 4 , 2 and 3 , 5 and 8 , 6 and 7 are pairs of vertical
angles.
3 and 6 and 4 and 5 are pairs of alternate interior angles.
Using angle relationships when two parallel lines are cut by a transversal, students are
expected to determine angle measures given the measure of one angle. Problems should
include algebraic expressions and equations (e.g., Given 3  3x and 6  x  30 , what is
the value of x? What is the measure of 3 ?)
Reflex angles measure more than 180° and less than 360º.
The relationships of angles may be verified by measuring the angles with a protractor, a
compass, or by physical direct comparison.
When drawing angles, students should use a protractor and straightedge.
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Updated: 8-29-16
Curriculum Information
SOL Reporting Category
Measurement and Geometry
Focus
Problem Solving
Virginia SOL 8.6
Foundational Objectives
6.12
The student will determine congruence
of segments, angles, and polygons.
5.11
The student will measure right, acute,
obtuse, and straight angles.
5.12a
The student will classify angles as right,
acute, obtuse, or straight.
Resources
Text:
Mathematics Course 3 VA Grade 8,
©2012, Prentice Hall, Pearson
Education
VDOE Enhanced Scope and Sequence
Sample Lesson Plans
http://www.doe.virginia.gov/testing/sol/sco
pe_sequence/mathematics_2009/index.php
Sample Instructional Strategies and Activities
 Use patty paper to trace angles and compare them with other angles to determine if they
are congruent.
 Given quilt square patterns, students will identify supplementary and complementary
angles.
 Students will verify measures of adjacent, vertical, complementary, and supplementary
angles by using a protractor.
 Students will draw angles (given the degree measure less than 360º) using a protractor
and straight edge.
Virginia Department of Education Website
http://www.doe.virginia.gov/instruction/ma
thematics/index.shtml
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Updated: 8-29-16