Special Triangles

Prepared by Title V Staff:Daniel Judge, Instructor

Ken Saita, Program Specialist

East Los Angeles College

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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

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

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