Five-Minute Check (over Lesson 5–5) Then/Now Theorems: Inequalities in Two Triangles Example 1: Use the Hinge Theorem and its Converse Proof: Hinge Theorem Example 2: Real-World Example: Use the Hinge Theorem Example 3: Apply Algebra to the Relationships in Triangles Example 4: Prove Triangle Relationships Using Hinge Theorem Example 5: Prove Relationships Using Converse of Hinge Theorem
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Lesson Menu Five-Minute Check (over Lesson 5–5) Then/Now Theorems: Inequalities in Two Triangles Example 1: Use the Hinge Theorem and its Converse Proof:
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Five-Minute Check (over Lesson 5–5)
Then/Now
Theorems: Inequalities in Two Triangles
Example 1: Use the Hinge Theorem and its Converse
Proof: Hinge Theorem
Example 2: Real-World Example: Use the Hinge Theorem
Example 3: Apply Algebra to the Relationships in Triangles
Example 4: Prove Triangle Relationships Using Hinge Theorem
Example 5: Prove Relationships Using Converse of Hinge Theorem
HEALTH Doctors use a straight-leg-raising test to determine the amount of pain felt in a person’s back. The patient lies flat on the examining table, and the doctor raises each leg until the patient experiences pain in the back area. Nitan can tolerate the doctor raising his right leg 35° and his left leg 65° from the table. Which leg can Nitan raise higher above the table?
Understand Using the angles given in the problem,you need to determine which leg can be risen higher above the table.
Solve Since Nitan’s legs are the same length and his left leg and the table is the same length in both situations, the Hinge Theorem says his left leg can be risen higher, since 65° > 35°.