Victory for the ACT Exam 16e TG Sample

508 • M ATH

STUDENT TEXT, p. 185 7. In the �igure below, what is the length of PQ ?

EXPLANATIONS

45° − 45° − 90° Triangles Items #7–8

7. (A) Mathematics/Geometry/Triangles/ 45° − 45° − 90° Triangles CC: HSG-SRT.C.6 CCRS: ADV.G.3 Difficulty Level = 2; Teaching Time = 5–8 minutes; Purpose = Example Te qhueatlr ai annggl el es ,hsaos iat irsi gah4t 5a°n g l e a n d t w o − 45° − 90° triangle. Thus, the length of PQ , one omfutlhteiplleiegds,bisyequal to the hypotenuse 2 2 0 (equivalent to division by 20 ): PQ PR 2 2 2 2 2 0 = = = ] ^ g h 2 2 1 = . Ao nl tearqnuaitcivkevlyi s, u“ ealli mc oimn aptaer- ai snodn-:g u e s s ” b a s e d PQ must be less than PR , which is equal to 2 0 . Tlehsesrtehfaonre, the correct answer must be 20 . The only answer choice that is less than 20 is 1, (A). 8. (G) Mathematics/Geometry/Triangles/ 45° − 45° − 90° Triangles CC: HSG-SRT.C.6 CCRS: ADV.G.3 Difficulty Level = 2; Teaching Time = 5–8 minutes; Purpose = Example In a 45° − 45° − 90° triangle, the hypotenuse ims uelqtuipallietod tbhye length of either leg 20 : s 20 . Ai slot es cr enlaetsi vter li ya,nsgi nl ec, et ht he el et gr isaanrgel ee qi suaanl i n length, s . Use the Pythagorean theorem: h s s 0 2 2 2 & h s h s 2 & = = = s 2 2 0 2 2 2 .

Don’t Forget This! Tanrigalnesglmesewasiuthring 4a r5e° , r 4i g5h° t, ai snods c9e0l °e s thryi apno gt el ensuws ei tehqau a l t o ts hi deel emnug ltthi pol fi eedi t bh ye r 20 .

A. 1 B. 2 0 C. 2 2 0 D. 4

8. Ihny pa orti egnh ut si seoissceeql eusatl rtioa nwghl ei c, ht hoef t h e following? F. Half the length of either of the other sides G. The length of either of the other sides multiplied by 2 H. Twice the length of either of the J. oTthheesrusmideosf the lengths of the other two sides

Teaching Tip Et on mc oeumr aogrei zset ut hdiesn t s pattern for 45° − 45° − 90° triangles. Su tsue dt ehne t Ps yc tahna ag lowr ea ay ns trhemeoermembe, br utht iisf they pattern for a 45° − 45° − 90° triangle, tvhaeluyawbliell tsiamvee on the exam.