Math 310 Ì SIM ILARITY Ì 8 123 123 12 123 12 12 123 23 1.Similar figures have the same shape but not necessarily the same size. W hich of the above are similar? CE D I2. “SSS” 110 121 77 77 121 99 63 G H A B F 90110IF the three sides of ÎABC are congruent to the respective sides of ÎDEF then ÎABC  ÎDEF .IF the lengths of the three sides of ÎABC and the corresponding sides of ÎGHI all f orm t he same RATIO,then the triangles are similar. We write: ÎABC ~ ÎGHI C F3. “SAS” I 100 100 80 40E 40E 40E A B D E G H 110 110 88If tw o sides and the included angle of ÎABC are congruent to the corresponding sides and included angle of ÎDEF then they are congruent— ÎABC  ÎGHIIf tw o sides of ÎABC and the corresponding sides of ÎGHI form the same ratio, and the included angles are congruent, then the two triangles are similar: ÎABC ~ ÎGHI 4. “ASA” C F I40E 60E 40E 60E 60E 40E A B D E G H ASA “AA”110 110W arning: W hat w orks for Triangles does not necessarily w ork for Quadrilaterals, or other figures.5. AAA ÿ similar triangles Recall: SSS ÿ congruent triangles butAAAA ÿ' similar quadrilaterals SSSS ÿ' congruent quadrilaterals. AD EH á á BC FGSince no “sideinformation” isneeded, it is not“ASA” theorem, it is “ AA”Which of these trianglesare congruent? Which aresimilar?Math 310 Ì SIM ILARITY cont’d Ì 6. Triangle ABC has congruent sides AB & AC. The midpoint of BC is "E". Is AE.an altitude of ªABC? A What triangles are congruent, and how do w e know ? What do w e know about pABE and pACE?What do w e know about pAEB and pAEC?B C E 7. Given that: A B is the midpoint of segment AD. C is the midpoint of AF. E is the midpoint of segment DF. B C What segments are parallel? What triangles are congruent, and w hy? D E F What triangles are similar, but not congruent?D 8. Points B & C “ cut” segment AD into thirds. C H Similarly F& I and H& J cut segments AK and DK into thirds. B G J What can be said about segments BJ and AK? What can be said about triangles BJD and AKD?A F I K If AB is 5u, then, since B & C cut AD in thirds, BD must be 2@5u, i.e. 10u, and AD must be 15u.If BJ is 12 u, then AK must be . A 9. a. b. E D c.*15 8 BC÷ 7 14 13 E D 5 C D15 21 A 56 9 B CA B Egiven: BC | | ED AB | | DE pA and pD are both right angles.All segments that appear straight are straight (including ACD and BCE in 2 and 3 sketches).nd rdWhat triangles are similar and w hy? Can you find the missing segment lengths? a. AD = b. AB = c. DE = BC = How w ould lengt h BCcompare to length EC ? Hint: How can w e find length AC?But do w e KNOW w hat EC is? BC? The SCALING factor fromÎDEC to ÎABC is ... 10. The sun is up in the sky, and casts a four-foot shadow for a five-foot tall person. At the same time, the shadow of the redw ood t ree is 70 f eet long. What is the height of the redw ood tree?geo_simf8Math 310 Ì SIM ILARITY some challenging problems Ì 1. If held 10" from the w all, a spray gun paints a disc 3" in diameter. How f ar f rom the w all should t he gun be held to spray a t oy that is 6" w ide? Additional, TOUGH QUESTION: * If at 10" w e spray for 1 second, at the new distance, how long should w e spray to get the same thickness of paint? F 110' 12. * Tom, Billy and Ann live in a straight line. Tom lives four blocks north and tw elve blocks west of Billy.Billy lives six blocks north of Ann. Explain exactly where Ann lives relative to Billy. (Hint: draw a map!) 13. * A 6' tall man standing 3' from a lamppost casts a shadow 4.5' long. How long would his shadow be if he stood 6' aw ay from the lamp? 14. Find t he dimensions of the out er triangle: 8mm ³13mm ³ 5 mm b12 mm 20.8 ,19.2,815. See Practice Final, Section