Thread: Bow Tie Shapes. Please help

Chuck used a dynamic geometry utility and kept drawing bow tie shapes. To do this, he used two parallel lines where A, and B are on one line, C and D are on the other. He moved only point D to change the shape. Elizabeth noted that no matter where he moved D, one thing remained true about the triangles making the bow tie. What did she observe about triangles ACE and DBE?

I don't know how to go about finding the solution. Can someone help me out please.

I can't imagine how she could observe anything about "triangles ACE and DBE" because there is NO point "E" in your picture or in your description of the problem.

Hello, Schuyla!

Chuck used a dynamic geometry utility and kept drawing bowtie shapes.
To do this, he used two parallel lines where A and B are on one line, C and D are on the other.
He moved only point D to change the shape.
Elizabeth noted that no matter where he moved D, one thing remained true about the triangles making the bowtie.
What did she observe about triangles ACE and DBE?

Code:

              C                 D
    - - - - - o - - - - - - - - o - -
             *|:*           *::*|
            *:|:::* E   *:::::* |
           *::|h::::o::::::::*  |h
          *:::| *     *:::::*   |
         *::* |         *::*    |
    - - o - - + - - - - - o - - + - -
        A     F           B     G

Draw altitudes and
Since

has base and height
has base and height
. . Hence, referring to areas: .

They both have in common.

Hence: .

Therefore: . . . . .

The two halves of the bowtie have equal areas.