Congruency and Triangles Featuring Right Triangles Section 4.6.
Special Triangles Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist...
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Special Triangles
Prepared by Title V Staff:Daniel Judge, Instructor
Ken Saita, Program Specialist
East Los Angeles College
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© 2002 East Los Angeles College. All rights reserved.
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Topics
45° – 45° – 90° Triangle 30° – 60° – 90° Triangle
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45° – 45° – 90° Triangle
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Consider a square with sides X.
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If we draw in diagonal we’ll obtain two triangles.
AC
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Take a closer look at the triangle ABC, it’s a Right Triangle!
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Applying the Pythagorean Theorem, we obtain the length of our diagonal .AC
2 2 2
2 2
2
Since (AC) X X
(AC) 2X
AC 2X
AC 2 X
AC X 2
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This is fundamental yet powerful result.
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Example 1)
becomes
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Example 2)
becomes
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Example 3)
becomes
Why?EXITBACK NEXTTOPICS
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Using the 45°- 45°- 90° relationship. . .
10 10 2X 2 10 X ; X
2 2 2
10 2 X
2
X 5 2
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Thus, if BC 10
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30° – 60° – 90° Triangle
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Consider an equilateral triangle.
We know equilateral triangles have: 1. Interior angles each measuring 60°. 2. All three sides have equal length.
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Bisecting angle ACB by drawing a line segment from vertex C to point D on side , we obtain the following:AB
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Now, represent the lengths of our equilateral triangle by 2X.
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We’ve created a 30°-60°-90° triangle.
We need to determine the length of one of our legs, it’s represented by the ?
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Using the Pythagorean Theorem,
2 2 2
2 2 2
2 2
2
? X (2X)
? X 4X
? 3X
? 3X
? 3 X
? X 3
We can now apply this result.
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Example 1)
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Example 2)
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Using,
152X 15; X
2
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Example 3)
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Using,
6X 3 6 or X
3
6 3 6 3X ; X
33 3
X 2 3
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End of Special Triangles
Title V East Los Angeles College
1301 Avenida Cesar ChavezMonterey Park, CA 91754
Phone: (323) 265-8784
Email Us At:[email protected]
Our Website:http://www.matematicamente.org
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