Loading...

PPT – Special Right Triangles-Section 9.7 Pages 405-412 PowerPoint presentation | free to download - id: 692703-NTFiM

The Adobe Flash plugin is needed to view this content

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 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.

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.

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

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.

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

The Easy Problems

The Moderate Problems

The Difficult Problems

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

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.