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Special Right Triangles-Section 9.7 Pages 405-412

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Special Right Triangles-Section 9.7 Pages 405-412 Adam Dec Section 8 30 May 2008 Introduction Two special types of right triangles. Certain formulas can be used to ... – PowerPoint PPT presentation

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Title: Special Right Triangles-Section 9.7 Pages 405-412


1
Special Right Triangles-Section 9.7 Pages 405-412
  • Adam Dec
  • Section 8
  • 30 May 2008

2
Introduction
  • Two special types of right triangles.
  • Certain formulas can be used to find the angle
    measures and lengths of the sides of the
    triangles.
  • One triangle is the 30-60-90(the numbers stand
    for the measure of each angle).
  • The second is the 45-45-90 triangle.

3
30- 60- 90
  • 30 - 60 - 90 - Triangle Theorem In a triangle
    whose angles have measures 30, 60, and 90, the
    lengths of the sides opposite these angles can be
    represented by x, x , and 2x, respectively.
  • To prove this theorem we will need to setup a
    proof.

4
The Proof
Given Triangle ABC is equilateral, ray BD
bisects angle ABC. Prove DC DB CB x x
2x
Since triangle ABC is equilateral, Angle DCB 60,
Angle DBC 30 , Angle CDB 90 , and DC ½
(BC) According to the Pythagorean Theorem, in
triangle BDC x (BD) 2x
x (BD) 4x

(BD) 3x BD x Therefore,
DC DB CB x x 2x
30
2x
60
90
x
5
45- 45- 90
  • 45 - 45 - 90 - Triangle Theorem In a triangle
    whose angles have measures 45, 45, 90, the
    lengths of the sides opposite these angles can be
    represented by x, x, x , respectively.
  • A proof will be used to prove this theorem, also.

6
The Proof
Given Triangle ABC, with Angle A 45 , Angle B
45 . Prove AC CB AB
x x x Both segment AC and segment BC are
congruent, because If angles then sides( Both
angle A and B are congruent, because they have
the same measure). And according to the
Pythagorean theorem in triangle ABC x x
(AB) 2x (AB) X AB Therefore, AC CB AB
x x x
x
x
7
The Easy Problems
8
The Moderate Problems
9
The Difficult Problems
10
The Answers
  • 1a 7, 7 1b 20, 10 1c 10, 5 1d
    346, 173 1e 114, 114
  • 5 11
  • 17a 3 17b 9 17c 6 17d 12
  • 21a 48 21b 6 6
  • 25a 2 2 25b 2
  • 27 40(12 5 ) 23

11
Works Cited
Rhoad, Richard. Geometry for Enjoyment and
Challenge. New. Evanston, Illinois Mc Dougal
Littell, 1991. "Triangle Flashcards." Lexington
. Lexington Education. 29 May 2008
lthttp//www.lexington.k12.il.us/teachers/menata/M
ATH/geometry/triangl esflash.htmgt.
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