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.
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>.