Posted by DANIELLE on Thursday, July 5, 2007 at 3:08pm.
Prove that the tangents to a circle at the endpoints of a diameter are parallel. State what is given, what is to be proved, and your plan of proof. Then write a twocolumn proof. Hint draw a DIAGRAM with the points labeled. Can some one please check for me
Given : ____________________________
To prove: _______________________________
Plan: ______________________________________
Given:
Lines AB and CD such that the lines are tangent to the circle with the center O at points B and D.
Segment BD is the diameter of the circle.
Prove:
Line AB is parallel to Line CD.
Plan:
Apply the parallel line property:
Two lines that are perpendicular to the same line are parallel.
Statements:
1) Line AB and Line CD are tangent to the circle
2) Segment BD is the diameter of the circle
3) Segment OB and Segment OD are the radii
4) Line AB is perpendicular to Segment OB; Line CD is perpendicular to Segment OD
5) Line AB is perpendicular to Segment BD; Line CD is perpendicular to Segment BD
6) Line AB is parallel to Line CD
Reasons:
1) Given
2) Given
3) Definition of a diameter
4) If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency.
5) Substitution property
6) Two lines that are perpendicular to the same line are parallel.
Your proof is excellent. I agree with all steps and reasons given. By "sustitution property" in statement # 5, iI assume you mean the reason is the same as #4

Geometry  beast, Tuesday, June 14, 2011 at 11:50am
Find the area of the larger segment whose chord is 8" long in a circle with an 8" radius.

Geometry  Anonymous, Tuesday, July 12, 2011 at 11:29am
Line AC is tangent to circle D at point B. Line HF is tangent to circle D at point E. Segments DB an DE are radii of circle D. Segment BC is congruent to segment EF.
Answer This Question
Related Questions
 Geometry  Write a twocolumn proof. Given: 7y=8x14; y=6 Prove: x=7 I need help...
 geometry  1)givenAB=CD,CD=EF proveABEF (in 5 steps that show why it is ...
 Geometry  Write a two column proof for: Given t is parallel s; angle 5 is ...
 Geometery  I am ask to write a two column proof. Given that AD is the diameter...
 geometry  Write a twocolumn proof. Given: 7y = 8x – 14; y = 6 Prove: x = 7
 geometry  Write a two column proof. Given CE = CA, EB and AD are medians, Prove...
 geometry  write a 2 column proof, Given D is the midpoint of AC, E is the ...
 geometry  ughh i need help i dnt like proofs we'll here it the instructions ...
 Geometry  Conditional Statements/Proof  Rewire each statement as two ifthen ...
 Geometry  Write a twocolumn proof. If point g is the centriod of triangle ABC ...
More Related Questions