anonymous
  • anonymous
In the figure below, ∠ABC ≅ ∠DEC and ∠GFE ≅ ∠DCE. Point C is the point of intersection between segment AG and segment BD, while point E is the point of intersection between segment AG and segment DF.
Mathematics
schrodinger
  • schrodinger
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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anonymous
  • anonymous
Prove ΔABC ~ ΔGEF.
anonymous
  • anonymous
1 Attachment
mathstudent55
  • mathstudent55
Here is the given figure. |dw:1440008861250:dw|

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mathstudent55
  • mathstudent55
Now let's add the given info.
mathstudent55
  • mathstudent55
|dw:1440008960006:dw|
mathstudent55
  • mathstudent55
Do you know how to prove triangles similar using only congruent angles?
anonymous
  • anonymous
AA triangle postulate?
anonymous
  • anonymous
mathstudent55
  • mathstudent55
Correct. Using vertical angles, we can do exactly that.
mathstudent55
  • mathstudent55
|dw:1440010430470:dw|
mathstudent55
  • mathstudent55
|dw:1440010452565:dw|
mathstudent55
  • mathstudent55
By using the theorem: "Vertical angles are congruent." we can show that the vertical angles shown in the figure are congruent. Then we have two angles of one triangle congruent to two angles of the other triangle, and by AA Similarity, we prove the two triangles are similar.
anonymous
  • anonymous
Okay, right
mathstudent55
  • mathstudent55
great
anonymous
  • anonymous
How would I put that into a paragraph proof?
anonymous
  • anonymous
mathstudent55
  • mathstudent55
By vertical angles,
anonymous
  • anonymous
Thank you so much!
mathstudent55
  • mathstudent55
You're welcome.

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