Victory for the ACT Exam 16e TG Sample

U NIT 4 | G EOMETRY • 507

TRIANGLES

Pythagorean Theorem Item #6

STUDENT TEXT, p. 185 6. In the �igure below, what is the length of AB ?

EXPLANATIONS

6. (H) Mathematics/Geometry/Triangles/ Pythagorean Theorem CC: 8.G.B.7 CCRS: AVG+.G.8 Difficulty Level = 2; Teaching Time = 5–8 minutes; Purpose = Example The �igure is a right triangle with a given lter iga onfg 3l e ai ns da h3y- 4p-o5t ePnyut hs ea goof r5e, asno ttrhi pi sl e , a n d the missing side has a length of 4. TPyhtihs aitgeomrecaanntahlesoorbeems: olved with the 5 3 & & BC AB AC AB 2 2 2 2 2 2 ^ ^ ^ ^ h h h h 16 2 ^ h Ab al tseerdn ao tni vtehl ey , i “nef loi mr mi naat it oe n- a pn rdo- vg iudeesds ”i n t h e dthraatwing. A quick visual comparison shows AB is larger than AC and smaller than BC . Therefore, AB must be more tbheaenl i3mai nn adt leeds,sl et ha va ni n 5g . aS o5 ,0(/F5)0a cnhda(nJ c) ec aonf guessing correctly. 25 9 16 4 & . AB AB

Don’t Forget This! Tt hheeo Pr eymt h as tgaotreesatnh e foIlnloawriinggh:t triangle, tl oh ne gseqsut asri ed eo f( tt hh ee heqyupaoltetonuthsee)siusm of toht he esrq tuwa roessi do ef st h e (the legs):

F G . . 2 2 3 H. 4 J. 4 2

a b c 0 2 2 2