5.6: inequalities in 2 triangles - msporod.weebly.com
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5.6: Inequalities in 2 Triangles
Use the Hinge Theorem & its converse to find a range of values for a given side or angle.
Think About It! The angle that a person makes as he or she is sitting changes with the task. The diagram shows
the position of a student as his desk. In which position is the angle measure at which he is sitting the greatest?
The least? Justify your answer.
Theorem Hypothesis Conclusion Hinge Theorem:
If 2 sides of one triangle are congruent to 2 sides of another triangle and the included
angles are not congruent, then the longer 3rd side is across from the _________________
included angle.
Converse of the Hinge Theorem
If 2 sides of one triangle are congruent to 2 sides of another triangle and the third sides
are not congruent, then the larger 3rd angle is across from the _________________________
included side.
Directions: Write an inequality to compare the given measures
Example 1: SR and PQ Example 2: mG and mL
Directions: Find a range of values for x
Example 3: Example 4:
Example 5: Example 6: Challenge!
Example 7: Two cyclists start from the same location and travel in opposite directions for 2 miles each. Then the
first cyclist turns right 90° and continues for another mile. At the same time, the second cyclist turns 45° left and
continues for another mile.
a) At this point, which cyclist is closer to the original starting point? Draw a picture to support your answer.
b) What is the range in distance from the starting point to where cyclist 1 currently is? Cyclist 2? Are they same
or different? Explain.