Geometry
posted by DANIELLE
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
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