How to Align Similar Polygons
How to Prove Triangles Similar with SAS~
How to Solve Similar Triangle Problems with the Side-Splitter Theorem

How to Use CASTC after Proving Triangles Similar

CASTC is simply an acronym that stands for ‘Corresponding angles of similar triangles are congruent.’ You often use CASTC in a proof immediately after proving triangles similar (in precisely the same way that you use CPCTC after proving triangles congruent).

image0.jpg

The following proof shows you how CASTC works:

image1.png

Here’s how your game plan might go: When you see the two triangles in this proof diagram and you’re asked to prove that the lines are parallel, you should be thinking about proving the triangles similar. Then, using CASTC, you’ve got congruent angles that you can use with the parallel-line theorems to finish.

So here’s the solution. You’ve got the pair of congruent vertical angles, angle 3 and angle 4, so if you could show that the sides that make up those angles are proportional, the triangles would be similar by SAS~ (Side-Angle-Side). So check that the sides are proportional:

image2.png

(Note that the similarity is written so that corresponding vertices pair up.)

image3.png
  • Add a Comment
  • Print
  • Share
blog comments powered by Disqus
How to Solve a Similar Polygon Problem
How to Use the Angle-Bisector Theorem
How to Solve Problems with the Altitude-0n-Hypotenuse Theorem
How to Prove Triangles Similar with SSS~
How to Prove Triangles Similar Using the AA Theorem
Advertisement

Inside Dummies.com