Wednesday
October 22, 2014

Homework Help: Geometry

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 two-column 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

Answer this Question

First Name:
School Subject:
Answer:

Related Questions

Plz Check my Geometry(sOo0n) - Out of 31 questions these are ones I struggled ...
Plz Check my Geometry(sOo0n) - Out of 31 questions these are ones I struggled ...
geometry - AB and AD are tangents of the circle with the center at C. The ...
Geometry - Circles and tangents - Two circles of radius 1 are externally tangent...
geometry - finish proof given ABCD is an isoceles trapezoid with AD parallel to ...
Plz Check my Geometry (Urgent) - ***I know I've posted this several times but it...
Geometry - in circle p below the lengths of the parallel chords are 20,16, and ...
geometry - Name the diameter, radius, center, and the equation of the circle ...
geometry - If the endpoints of the diameter of a circle are (3, 1) and (6, 5), ...
geometry - a circle has diameter endpoints of A(5,10) and B(-3,4). what are the ...

Search
Members