University:
Felician University
Course:
MATH-231 | Geometry I
Academic year:

2022
Views:

205

Pages:

6
Author:

5CelestialChronicle

Triangle Proportionality Theorem {Side�Splitter) Theorem Triangle Proportionality Theorem lf а line parallel to one side of а triangle intersects the other two sides of the triangle, then the parallel line divides these two sides proportionally. в - �----- --· ·------·--/�О СЕ ln the figure above, АС II DE; therefore, - = - . DB ЕВ с · ·- Example 1 в в А А с -- �.S 2.. ьх::: 3 5,5) 3 2. Example З Solve for х 9 Е 12 • iх i ! l_ . 1 ! х -\2.. 'р i 1х_ == 120 15 � === Example 4 Example 5 в 10.5 D Е 3 А А tJ � -• , (;,.s -3g,5 3 - 9 5.25 -. 3-? 360.5 f(5.2.S с 7 '3 . S, / $11М 11,1\t, / 31.S ¾:+5 L..-...-------� .де_ '1E.S � Triangle Angle Bisector Theorem (А ngle-5 р I itter) Theorem Triangle Angle Bisector Theorem lf one angle of а triangle 8 is Ьisected, ог cut in half, then the angle blsector of the triangle divides the opposite side of the triangle into two segments that аге proportional to the other two sides of the triangle. с А '-- -� АО ВА L�l:3C therefore - = • .дВо � J)BG ""Stм � ос ас 6 s Exampie 6 • Let 1s just look at how we would set this up. • Find the lengths of BD and DC . 7 7&-+1 = G-tt,(Y-+ � С{�-+ 1- == G toX + l . 2 1 Lf� ::: ч. 2 7 )(::: � Similar Right Triangles lf an altitude is drawn to the hypotenuse of а right triangle, then the two triangles formed are similar to the original triangle and each ч.i L\.\ � +- L, в с - f.o -�ц:ъ �) е.. � й> о i Lf.i_ � � е -= ·f f_ :::: ...-=- ч-.ъ � 'g -;::::::.. t f' �:ц,J XL tip: find the !Leometric me�n of 5 and 12. Leave your answer as а reduced radicai. XL tip: find the geometric mean of 3 and 10 to the nearest 10th. 30 11 When do you use the Geometric Mean? • When you are looking for а missing side AND • you have а right triangle AND • The triangle is divided with an altitude