Download Classifying Triangles(CC.6.G.5)

Lesson 90
California Saxon Math 6
Classifying Triangles (CC.6.G.5)
At the end of Lesson 90 complete the following activity.
In Lesson 90 we learned how to classify a triangle using information about the angles and/or sides. In this activity, you
will use geometry software to construct triangles.
Draw a triangle whose sides have lengths of 2 units, 3 units, and 4 units.
Step 1: Draw the longest side first. Use the line segment
tool to draw line segment AB with a length of 4 units.
Step 2: Use the circle tool to draw a circle with its center
at point A and a radius of 2 units.
Step 3: Use the circle tool to draw a circle with its center at
point B and a radius of 3 units.
Step 4: The circles intersect at two points. Choose one of the
intersection points to be point C, and draw line segments
AC and BC to complete the triangle. (No matter which of
the two points you choose, the triangle will have the same
measurements, so there is really only one possible triangle.)
C
A
B
Draw a triangle with two angles that measure 50° and 70° and an included side that measures 5 units.
Step 1: Use the line segment tool to draw line segment AB with a
length of 5 units.
Step 2: Use the angle tool to draw a 50° counterclockwise angle
from segment AB with a vertex at A. Drawing this angle
creates point C. Draw a ray with an endpoint at A through point C.
Step 3: Use the angle tool to draw a 70° clockwise angle from segment AB
with a vertex at B. Drawing this angle creates point D. Draw a ray
with an endpoint at B through point D.
Step 4: The point where rays AC and BD intersect is the third vertex of the triangle.
D
50°
A
5 units
C
70°
B
Draw a triangle with two sides that measure 4 units and 3 units and a 30° angle that is not between the given
sides.
C
Step 1: Use the line segment tool to draw line segment AB with a
length of 4 units.
Step 2: Use the angle tool to draw a 30° counterclockwise angle
from segment AB with a vertex at A. Drawing this angle
30°
creates point C. Draw a ray with an endpoint at A through point C.
B
A
Step 3: Use the circle tool to draw a circle with its center at point B and a
radius of 3 units.
Step 4: Draw line segments to form the two distinct triangles.
If you can draw more than one triangle that satisfies given conditions, the conditions are ambiguous.
Activity Master
Name: __________________________________
For use with Lesson 90 Extension Activity
Classifying Triangles
Use geometry software to draw ΔPQR that matches the given conditions. If no triangle has these conditions, write not
possible. If exactly one triangle has these conditions, write unique. If more than one triangle has these conditions, write
ambiguous.
1. PQ = 2 units, QR = 4 units, PR = 7 units
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2. PQ = 4 units, QR = 6 units, PR = 10 units
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3. PQ = 3 units, QR = 8 units, PR = 6 units
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4. PQ = 4 units, QR = 5 units, m∠Q = 45°
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5. m∠Q = 50°, m∠R = 45°, QR = 4 units
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6. m∠P = 40°, m∠Q = 40°, QR = 3 units
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7. m∠P = 30°, PR = 3 units, QR = 2 units
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8. m∠P = 60°, PR = 3 units, QR = 2 units
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9. ∆PQR is equilateral with perimeter 9 units
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10. ∆PQR is isosceles with perimeter 9 units
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11. If the measures of two angles and the length of the side between them is given, will the measurements always
result in a triangle? Explain.