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5.5 Problem Solving Help

Lesson 5.5: Help for Exercises 33 and 34 on page 300

For Exercise 33, the proof is already set up. If you use the given statement along with the given diagram to prove that , you will have proved a perpendicular segment is the shortest line segment from a point to a line. Consider using the definition of perpendicular lines, the definition of a right angle, and the Triangle Sum Theorem to show that . Then apply a theorem from this lesson to conclude .

For Exercise 34, it may be difficult to see the direction of the proof until it is nearly complete. Try to fill in the blanks as you read the numbered statements and reasons. Statement 6 follows from Statements 4 and 5; this may help you fill in the blank for Statement 5. For Statements 6 and 7, focus on . For Statement 8, use Statement 7 but substitute for DC. For Statement 9, use Statement 8 but substitute for AD.