Thursday

April 17, 2014

April 17, 2014

Posted by **DANIELLE** on Thursday, July 5, 2007 at 3:08pm.

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 11:50amFind 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 11:29amLine 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.

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