• Support PF! Buy your school textbooks, materials and every day products Here!

Help with Geometry

  • Thread starter Tanya Back
  • Start date
  • #1
18
0
Hey Guys! I am really stuck on this questions:

The medians BD and CE in triangle ABC are produced to X and Y respectively so that BD=DX and CE=EY. Prove that X,A, and Y lie in a straight line.

I tried this question, it made no sense to me...i drew the picture and i named the interesting point between BD and CE "F". Then i proved that Traingle BYF is congruent to triangle CXF (SAS)...and then i have noo clue wut to do..PLz Help!!

Thank u!
Tanya
 

Answers and Replies

  • #2
Andrew Mason
Science Advisor
Homework Helper
7,560
323
Tanya Back said:
Hey Guys! I am really stuck on this questions:

The medians BD and CE in triangle ABC are produced to X and Y respectively so that BD=DX and CE=EY. Prove that X,A, and Y lie in a straight line.
Look at AXD and BCD and at AYE and BCE. Show that AX is parallel to BC and AY is parallel to BC (look at corresponding angles). If you can show this, then since AX and AY are parallel to the same line and share a common point, XAY would have to be a straight line.

You can also show that XAC = ACB and CBA = BAY. Since CAB is the third angle in triangle ABC, ACB + CBA + CAB = 180 = XAC + BAY + CAB. The last three angles sum to XAY which means that XAY is a straight line (180 degrees).

AM
 

Related Threads for: Help with Geometry

  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
7
Views
830
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
11
Views
4K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
4
Views
1K
Replies
4
Views
4K
Top