Your SlideShare is downloading. ×
Proving lines are perpendicular
Upcoming SlideShare
Loading in...5
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×
Saving this for later? Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime – even offline.
Text the download link to your phone
Standard text messaging rates apply

Proving lines are perpendicular

10,769

Published on

Published in: Education, Technology, Business
0 Comments
1 Like
Statistics
Notes
  • Be the first to comment

No Downloads
Views
Total Views
10,769
On Slideshare
0
From Embeds
0
Number of Embeds
0
Actions
Shares
0
Downloads
25
Comments
0
Likes
1
Embeds 0
No embeds

Report content
Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
No notes for slide

Transcript

  • 1. Proving Lines are Perpendicular
  • 2. Properties of Perpendicular Lines Perpendicular Lines Postulate: • l1⊥l2 if and only if m1∙m2 = -1 • That is, m2 = -1/m1, The slopes are negative reciprocals of each other. • Two non-vertical lines are perpendicular if and only if the product of their slopes is -1. Vertical and horizontal lines are perpendicular.
  • 3. • In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other. Theorem: Perpendicular to Parallel Lines: and Then
  • 4. • If two coplanar lines are each perpendicular to the same line, then they are parallel to each other. Theorem: Two Perpendiculars:
  • 5. Proof of Perpendicular to Parallel Lines Theorem Statement Reason 1 l ll m, l ⊥ n Given 2 ∠1 is a right angle Definition of lines⊥ 3 m∠1 = 90o Definition of a right angle 4 m 2∠ = m∠1 Corresponding angles postulate 5 m∠2 = 90o Substitution property of equality 6 ∠2 is a right angle Definition of a right angle 7 m ⊥ n Definition of lines⊥ Given: l ll m and l ⊥ n Prove: m ⊥ n
  • 6. Examples 1. Line r contains the points (-2,2) and (5,8). Line s contains the points (-8,7) and (-2,0). Is r ⊥ s?
  • 7. 2. Given the equation of line v is and line w is Is v ⊥ w?
  • 8. Given the line 3.Find the equation of the line passing through ( 6,1) and perpendicular to the given line. 4. Find the equation of the line passing through ( 6,1) and parallel to the given line.
  • 9. Homework • Exercise 3.7 page 175: 1-35, odd.
  • 10. Homework • Exercise 3.7 page 175: 1-35, odd.

×