Victory for the ACT Exam 16e TG Sample

U NIT 4 | G EOMETRY • 517

STUDENT TEXT, p. 188 21. Aa nc i irscol es cwe li et hs rai gr ahdt itursi aonfg1l ei ni sc hi nssuc rc ihb tehdaitn ao lnl tthhreecei rvcel ret. iWc ehs aotf itshteh ter ai arne ga l, ei na rseq upaori en t s inches, of the triangle? A. 3 2 B. 2 1 C. 1 D. 2 0

EXPLANATIONS 21. (C) Mathematics/Geometry/Complex Figures and Circles and Triangles/ Properties of Triangles CC: HSG-MG.A.1 CCRS: ADV.G.3 Difficulty Level = 2; Teaching Time = 5–8 minutes; Purpose = Walkthrough The correct choice is (C), which is more easily seen if a �igure is drawn:

To fh teh de i tarmi aent ge lre o. Hf tohwe ecvi re cr ,l ea ni s aal lt si tou tdhee i bs a s e needed, so add it:

Tc ihr ce l et r’ si arnagdl ieu’ ss , h1e. i Tg hh tu iss, tehqeu tarl i taon gt hl ee’ s a r e a is bh 2 2 2 1 1 = = ] g . 22. (H) Mathematics/Geometry/Complex Figures and Triangles/Properties of Triangles and Rectangles and Squares CC: HSG-MG.A.1 CCRS: AVG+.G.5 Difficulty Level = 2; Teaching Time = 5–8 minutes; Purpose = Application Triangle ABE has three 60° angles, so it is an equilateral triangle. To �ind the ps iemr ipml ye tdeert eorf ma ni neeqtuhiel alteenr ga tl ht roi af nognlee ,s i d e ag ni vde nmiunl ttihpel yi tbeym3i.sTthhee oanr el ya ionff ot hr me saqt iuoanr e . Ns i od tei coef tt hh ae t t or inaen gs il de .eSoi nf ct he et hs eq us aq ruea ri se ’asl saor eaa is 4, the side of the square is 2 ( area = square s s 4 2 & = = = 4 2 ). Thus, the triangle’s perimeter is: s 03 = 3(2) 6 = .

22. In the �igure below, BCDE is a square with an area of 4. What is the perimeter of ABE T ?

F. G. 4 3 H. 6 J. 8