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Drawing Triangles SAS
Resource ID#: 70695
Primary Type: Formative Assessment
This document was generated on CPALMS - www.cpalms.org
Students are asked to draw a triangle given the measures of two sides and their included angle
and to explain if these conditions determine a unique triangle.
Subject(s): Mathematics
Grade Level(s): 7
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, included angle, triangle
Instructional Component Type(s): Formative Assessment
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_DrawingTrianglesSAS_Worksheet.docx
MFAS_DrawingTrianglesSAS_Worksheet.pdf
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
This task can be implemented individually, with small groups, or with the whole class.
1. The teacher asks the student to complete the problems on the Drawing Triangles
SAS worksheet.
1. The teacher asks follow-up questions, as needed.
Note: The teacher should explain the meaning of included angle and nonincluded angle if these
terms are unfamiliar to the student.
TASK RUBRIC
Getting Started
Misconception/Error
The student is unable to draw a triangle with the given conditions.
Examples of Student Work at this Level
The student:

Draws a triangle with incorrect angle or side measures.

Draws a figure that is not a triangle (e.g., an open figure with three sides).
Questions Eliciting Thinking
What are the features of a triangle?
What is an included angle?
What strategies would you use to draw a triangle given the measures of two sides and the
included angle? Where is a good place to begin drawing?
How would using the ruler and protractor help you draw a triangle with the given conditions?
Instructional Implications
Define a triangle as a polygon with three sides. Make clear that an open figure with three sides
is not a triangle (since it is not a polygon). Describe the parts of a triangle and how to name
them (e.g., the vertices, sides, and angles). Be sure the student understands how to measure
angles.
Provide the student with a manipulative such as
or software such as Geogebra
(www.geogebra.org) to assist in building triangles with given conditions. The student may be
more adept in drawing triangles with given conditions after working with a hands-on
manipulative or software.
Guide the student to draw a triangle with given conditions. Assist the student in using the ruler
and protractor to construct the triangle. Explain that a good way to begin is by drawing a
working line and "building" the triangle on it. Ask the student to measure one of the given
lengths (e.g., 1
in.) on the working line and label this as
the student measure and draw
. Using point E as a vertex, have
. Next, have the student measure and mark the endpoint of
on the other side of
using the second given length. Then have the student draw to form
the third side of the triangle. If needed, model how to properly label the angles and sides of a
triangle. Finally, have the student verify that the drawn triangle fits the given conditions.
Provide additional opportunities for the student to draw triangles when given the measures of
two sides and their included angle.
Moving Forward
Misconception/Error
The student is unable to correctly determine if the given conditions form a unique triangle.
Examples of Student Work at this Level
The student is able to draw a triangle with the given conditions, but says it is possible to draw
a different triangle with the same conditions. For example, the student states:

The triangles are not the same (e.g., congruent) because they are oriented differently.

The shapes will be similar.

A new triangle can be drawn if the same measurements are put on different sides.
Questions Eliciting Thinking
What do you mean by "the shapes will be similar?"
What would be different in the new triangle?
Can you change the measure of an angle without affecting the length of its opposite side?
Can you change the measure of a side without affecting the size of the opposing angle?
Instructional Implications
Use tracing paper to demonstrate to the student that two triangles can be oriented differently
but still be the same (e.g., congruent). If the student did not attempt to construct a second
triangle with the given conditions, ask the student to do so. Have the student confirm that the
measures of the sides and angles correspond to the given measures. Then have the student use
tracing paper to determine if the triangles are congruent.
Another option is to have the student imagine changing the length of side and the effect this
would have on the measure of the opposite angle,
. Guide the student to observe that
changing the measure of the side of a triangle causes the measure of the opposite angle to
change as well. Since
must measure 100°, the length of the opposite side cannot take on a
different measure.
Provide the student with another set of SAS conditions, and encourage the student to further
experiment and confirm this conclusion.
Almost There
Misconception/Error
The student does not adequately explain why the given conditions form a unique triangle.
Examples of Student Work at this Level
The student is able to draw a triangle with sides of the given lengths and says it is not possible
to draw more than one triangle with these conditions, but does not provide a clear explanation.
The student explains:

The triangles will be the same.



You can only draw the triangle one way.
The angles (or sides) would all be the same.
You are not able to change one angle or side without changing another side or angle.
Questions Eliciting Thinking
Can you explain why the triangles will be the same?
Are there some sets of conditions that do not determine a unique triangle?
Instructional Implications
Help the student confirm his or her conclusion by constructing another triangle with the same
three measurements. Have the student directly measure the angles and compare the
measurements to the angle measures of the original triangle. Guide the student in discussing
the relationship among the sides and angles within a triangle.
Model constructing a triangle with sides and included angle of the given measures as described
in the Getting Started Instructional Implications. Show the student that the length of the third
side is determined by the given angle measure. Explain that this ensures that there is only one
way to draw the triangle. Model a concise explanation using mathematical terminology. For
example, if
is 100°, and its side lengths are 1 inches and 2 inches in length, all three
vertices of the triangle have been determined. This means there is only one possible length for
the third side, and a unique triangle is determined.
Got It
Misconception/Error
The student provides complete and correct responses to all components of the task.
Examples of Student Work at this Level
The student is able to draw a triangle with the given angle and included side measures and says
it is not possible to draw more than one triangle with these conditions. The student explains in
terms of:


The uniqueness of the third side (see Instructional Implications for Almost There).
The relationship between the length of a side and the opposite angle measure.
Questions Eliciting Thinking
If sides
and
were switched, would the triangle be congruent to the original? Explain.
What does "congruent" mean?
Can you describe your strategy in drawing triangle DEF?
How important was accuracy and precision in completing this task?
Instructional Implications
Pair the student with a Moving Forward partner to share strategies for drawing triangles.
Consider implementing the MFAS tasks Drawing Triangles ASA, Drawing Triangles AAA,
Drawing Triangles SSA, Drawing Triangles AAS, or Drawing Triangles SSS (7.G.1.2).
ACCOMMODATIONS & RECOMMENDATIONS

Special Materials Needed:
o
o
o
o
Drawing Triangles SAS worksheet
Ruler
Protractor
Technology such as Geogebra (optional)
SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
District/Organization of Contributor(s): Okaloosa
Is this Resource freely Available? Yes
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.7.G.1.2:
Description
Draw (freehand, with ruler and protractor, and with technology)
geometric shapes with given conditions. Focus on constructing
triangles from three measures of angles or sides, noticing when
the conditions determine a unique triangle, more than one
triangle, or no triangle.