Question

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In the figure below, ΔABC ≅ ΔDEF. Point C is the point of intersection between segment AG and segment BF while point E is the point of intersection between segment DG and segment BF.


http://learn.flvs.net/webdav/assessment_images/educator_geometry/v15/module05/05_08_1b.jpg

Prove ΔABC ~ ΔGEC.

Answer 1

@guruslimm: Here's a word to the wise: I cannot open and view your illustration.

Answer 2

You may have to do a screen capture and then attach the image to this discussion.

Answer 3

@mathmale thank you

is the image there now

Answer 4

Yes. Now I can see it (although it's awfully small and hard for old eyes to decipher). :)

Answer 5

you are told that the two largest triangles are congruent (equal in size and shape to each other). That means that the corresponding angles in the two triangles are equal, as well as that the corresponding sides are equal.

You are to prove that the larger triangle on the left is similar to (but not congruent to) the little triangle GEC.

Answer 6

What are y our thoughts so far?

Answer 7

To be honest I'm not really god with proofs, I can only answer a question like this correctly if there are options that way I can eliminate the wrong ones

Answer 8

It's been many years since I used the proper terminology in geometric proofs, but I do remember a lot of the impotant principles.

Angles BCA and ECG are (what kind of) angles?

See: http://www.mathsisfun.com/geometry/vertical-angles.html

Answer 9

i know that they are vetical angles & angle FED & GEC are also vertical angles

Answer 10

Are they therefore equal, or not?

Answer 11

Vertical angles are always equal.
Look carefully at what we've done so far. List what you know about the large triangle on the left and the small triange in the middle. What further evidence might you need to prove that these two triangles are similar?

Answer 12

angle BCA &ECG are vertical angles
angles in triangle ABC and EGC are congruent
two of their sides are intersecting each other