University:
High School
Course:
High School Algebra
Academic year:

2022
Views:

42

Pages:

2
Author:

Lilly Hardy

Similar Right Triangles Core Concepts Geometric Mean The geometric mean oftwo positive numbers а and Ь is the positive number х that а satisfies - х х - So ь :::: '='". an.d Theorems Theorem 9.6 Right Triangle Similarity Theorem Ifthe altitude is drawn to the hypotenuse ofа right triangle, then the two triangles formed are similar to the original triangle and to each other. с лсвп~ллвс, /1\ л А l '"\.. в D . D с с А L 1'!, ,,._11-� \ 'J с � OL."-c..A- �iJ.•-<.. �...,....,\\ С в А в D D В and and ЛАСD~ЛАВС, с � LD"--�'1 ф j '\.. с • с. 8 с Ас,.,,_4� D �-·i-.- А ЛСВD~ЛАСD .1\,,,4- ""' с.. ��о с.о В . • D· .,�с D А � А в Theorem 9.7 Geometric Mean (Altitude) Theorem In а right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments. The length ofthe altitude is the geometric mean ofthe lengths ofthe two segments ofthe hypotenuse .. Vv�.... аН·· D ь В с � о•,,..., ·"'''Г•' °t' �� , c..D CDz =AD•BD· со Theorem 9.8 Geometric Mean (Leg) Theorem In а right triangle, tl1e altitude from tl1e right angle to tl1e hypotenuse divides the hypotenuse into two segments. r . с/ �-1 The length ofeach leg ofthe right triangle is the geometric mean ofthe lengths ofthe hypotenuse and the segmeпt of the hypotenuse tl1at is adjacent to the leg. с 22 А D � �� llOJ в с �'5 А ,J-"'' В ,�� -ь �. "\'/' ;;> _,...____,.....__� -0: leJ =, =---Р /tC.. . : .• / ,.. Ai?J 4с. __...,_,___,, С.13 ·Dr� .,,---�-.... ь АС2 = AD • А.В, � се, св 2 �1 '------·/ = DB•• АВ tJ 1 �i,(� / ( Extra Practice \\ .t \ ,е:"\' ,,. \._ __-1' 1\' ·� ln Exercises 1 and 2, identify the similar triangles "-} 1' J ЛJ tI rvдK:Y.I. А :11-1 1: 1 ,....,_ д оР /11 "-,, А" PAJ 2. о�=-=:::::.__пр�?==�;;:__-N !J r. Н- :У � о Р /1\ 1'\.,-Л D 11\ А) дм PN �д off\� н ln Exercises 3 and 4, find the geometric mean of the two numbers. 4. 5 and 3. 2 and 6 -ь р -- '} ,_ ;;';) 1,.,) ь / rn=- / it 1' J- р (..,J р '3 6 Р· ь v\ s е. е variaЫe. H-t.. �1�-k.L� • �е.) (,'\, f,q r\ ��ь и. [s, q.5 :: р'- СО) -; . р чs -;:. / /� � р ! 'Х q ( l Ь� 1·-------lb J� 1 - • ·�· •• 1� - - . .J ЧSl �� 1�� C\.S 6. al+ q - 'r- .,,., ,...._ �� р (р') 5( (.J i') ·- 1 ln Exercises 5-8, find the va е о 5. i1 r -- i(ro'):.p(p -�- ? � 45 l.t>c, ч с,�() м t''11'\ , t4' 1 \l 'i -:..- � 'Х. ( ?<-') -:. х 1. и� i_�J 3,ч 7. t �� - .ь._у_ р ц 'i'l - - а r-1" " 8. al+ /� i: 7 '1'1 .t•1q(�t'1):. 7{{) - ·1 .. ·,1"· / (1-t q\;; t t7 / 3ч 3-:- "3/о: + '1) �- --- Ct -f /,( �-ч 1 ·:� ...;Ч _. -.. - lj