logo for solving-math-problems.com
leftimage for solving-math-problems.com

ANGLES AND LINES

by NOUR TMH
(BEYROUTH, LEBANON)

let OBM be an isoscoles trianle with vertex O.C is a point of [OB] and N is a point of [OM] such that OC=ON.draw a figer corresponding to the given data.prove that (CN) is parallel to (BM)

let OBM be an isoscoles trianle with vertex O.C is a point of [OB] and N is a point of [OM] such that OC=ON.draw a figer corresponding to the given data.prove that (CN) is parallel to (BM)










































let OBM be an isoscoles trianle with vertex O.C is a point of OB and N is a point of OM such that OC=ON.draw a figer corresponding to the given data.prove that (CN) is parallel to (BM)

Comments for ANGLES AND LINES

Click here to add your own comments

Feb 09, 2012
Prove Lines Parallel
by: Staff

Question:

by NOUR TMH
(BEYROUTH, LEBANON)



let OBM be an isosceles triangle with vertex O.C is a point of OB and N is a point of OM such that OC=ON.draw a figer corresponding to the given data.prove that (CN) is parallel to (BM)



Answer:


Open the following link to view the triangle:


(1) If your browser is Firefox, click the following link to VIEW ; or if your browser is Chrome, Internet Explorer, Opera, or Safari (2A) highlight and copy the link, then (2B) paste the link into your browser Address bar & press enter:

Use the Backspace key to return to this page:

http://www.solving-math-problems.com/images/triangle-isosceles-01-2012-02-09.png


This is not a formal proof, but it is a good explanation which can form the basis for a formal proof:


Since ΔOMB is an Isosceles Triangle, it has two congruent sides and two congruent angles (two congruent base angles).

In this case:

Given:

∠OMB ≅ ∠OBM

OM ≅ OB

ON ≅ OC

Since ON ≅ OC, ΔONC is also an isosceles triangle which shares ∠O with Δ MOB

∠NOC ≅ ∠MOB

Since ∠NOC ≅ ∠MOB, the corresponding angles ∠ONC ≅ ∠OMB


Corresponding Angle Equivalence Implies Parallel Lines


If ∠ONC ≅ ∠OMB, then NC∥MB



Thanks for writing.

Staff
www.solving-math-problems.com



Click here to add your own comments

Join in and write your own page! It's easy to do. How? Simply click here to return to Math Questions & Comments - 01.



Copyright © 2008-2015. All rights reserved. Solving-Math-Problems.com