Sum of the measures of the two shorter sides > the measure of the third side.
Example: line segments a, b, c with measures 3 inches, 4 inches, and 5 inches.
a + b (7) > c (5) forms a unique triangle.
No triangle is formed if:
Sum of the two shorter sides ≤ the measure of the third side.
Included Side
Defined as the side of a polygon between two given angles.
Example: Segment AC is the included side between Angle A and Angle C.
Using a Protractor
Protractor has degree measures on both the outside and inside of its curve.
Place the hole in the center of the protractor on the vertex of the angle.
Align the base with the line to measure the angle.
Different scales (inside and outside) are used depending on the orientation of the angle.
Drawing Triangles with Given Measures
Using a Ruler and Protractor:
Given angles: 40° and 60°, included side length: 5 inches.
Draw a 5-inch line segment.
Measure and mark 40° using inside scale, draw ray.
Measure and mark 60° using outside scale, draw ray.
Result: Triangle with angles 40°, 60° and included side 5 inches.
Second Triangle Example:
Angles: 50° and 70°, included side: 3 inches.
Draw 3-inch side.
Measure, mark, and draw 50° (inside measures) and 70° (outside measures) angles.
Result: Unique triangle.
Unique and Non-Unique Triangles
Unique triangle formed when angles and included side are specified.
Non-unique triangles when multiple triangles can be formed from the same angle measures but different side lengths.
Example: Triangles with angles 30°, 60°, 90° are not unique as they can be scaled versions of each other, e.g., differing base lengths of 4 inches and 6 inches.
Conclusion
A triangle is unique when the sum of the measures of the two shorter sides exceeds the measure of the third side.
The lesson will continue with cross sections in the next session.