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Chapter 3

Chapter 3. 3-4 Perpendicular Lines. SAT Problem of the day. A cube has a surface area of 6x. What is the volume of the cube? A) B) C) D) E). Solution to the SAT Problem. Right Answer: B. Objectives. Prove and apply theorems about perpendicular lines.

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Chapter 3

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  1. Chapter 3 3-4 Perpendicular Lines

  2. SAT Problem of the day • A cube has a surface area of 6x. What is the volume of the cube? • A) • B) • C) • D) • E)

  3. Solution to the SAT Problem • Right Answer: B

  4. Objectives • Prove and apply theorems about perpendicular lines.

  5. What is the perpendicular bisector? • The perpendicular bisectorof a segment is a line perpendicular to a segment at the segment’s midpoint.

  6. Distance from a point to a line • The shortest segment from a point to a line is perpendicular to the line. This fact is used to define the distance from a point to a lineas the length of the perpendicular segment from the point to the line.

  7. Example#1 A. Name the shortest segment from point A to BC. The shortest distance from a point to a line is the length of the perpendicular segment, so AP is the shortest segment from A to BC.

  8. Example#1 • B. Write and solve an inequality for x. • AC > AP • x – 8 > 12

  9. Example#2 A. Name the shortest segment from point A to BC. AB is the shortest segment from A to BC. B. Write and solve an inequality for x. AC > AB 12 > x – 5

  10. Student guided practice • Do problems 2 and 3 from your book page175

  11. HYPOTHESIS CONCLUSION

  12. Proving perpendicular lines • Write a two-column proof. • Given: r || s, 1  2 • Prove: r  t

  13. solution 1. Given 1.r || s, 1  2 2. Corr. s Post. 2.2  3 3.1  3 3. Trans. Prop. of  4. 2 intersecting lines form lin. pair of  s  lines . 4.rt

  14. Given: Prove: Proving perpendicular lines • Write a two-column proof.

  15. 2. 3. 4. 1. Given 1.EHF HFG 2. Conv. of Alt. Int. s Thm. 4. Transv. Thm.

  16. Student guided practice • Do problem 4 in your book page 175

  17. Homework • Do problems 6- 8,12-15 in your book page 175 and 176

  18. closure • Today we learned about perpendicular lines • Next class we learned about slopes of lines

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