Similar Triangles I - PowerPoint PPT Presentation

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Similar Triangles I. Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist East Los Angeles College. Click one of the buttons below or press the enter key. BACK. NEXT. EXIT. © 2002 East Los Angeles College. All rights reserved.

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Similar Triangles I

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Similar Triangles I

Prepared by Title V Staff:Daniel Judge, InstructorKen Saita, Program SpecialistEast Los Angeles College

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In geometry, two polygons are similar when one is a replica (scale model) of the other.

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Consider Dr. Evil and Mini Me from Mike Meyers’ hit movie Austin Powers. Mini Me is supposed to be an exact replica of Dr. Evil.

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Triangles are a class of polygons in geometry. Therefore we can talk about triangles that are similar. The following is a picture of similar triangles.

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Note: One triangle is a scale model of the other triangle.

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Q: How do we truly know that the above two triangles are similar (scaled model)?

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Answer– We must take a closer look at the sides of our triangles. The following conditions must all be satisfied.

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1.

2.

3.

Scaling Factor

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This can all be summarized as:

Scaling factor

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Our problem becomes as follows:

Scaling factor

This tells us that  ABC and  XYZ are similar.

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Q: Can these triangles be similar?

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Answer—Yes, right triangles can also be similar but use the criteria.

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Do we have equality?

This tells us our triangles are not similar. You can’t have two different scaling factors!

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Q: The two triangles below are known to be similar, determine the missing value X.

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Answer– Using the fact that our triangles are similar . . .

The missing side has a length that’s 3 units. The picture should look like this . . .

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Q: The following triangles are similar. Can you determine the missing sides X and Y?

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Our triangles should look like this:

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Let’s take a closer look at the criteria that tells us when triangles are similar:

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Mathematicians find this next relationship useful as well.

Why?

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End of Similar Triangles ITitle V East Los Angeles College1301 Avenida Cesar ChavezMonterey Park, CA 91754Phone: (323) 265-8784Email Us At:menteprog@hotmail.comOur Website:http://www.matematicamente.org

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