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.
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30 May 2008
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
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
Rhoad, Richard. Geometry for Enjoyment and Challenge. New. Evanston, Illinois: Mc Dougal Littell, 1991.
"Triangle Flashcards." Lexington . Lexington Education. 29 May 2008 <http://www.lexington.k12.il.us/teachers/menata/MATH/geometry/triangl esflash.htm>.