Regents Exam Questions G.SRT.B.5: Similarity 1 Name: ________________________ www.jmap.org G.SRT.B.5: Similarity 1 1 Triangle JGR is similar to triangle MST . Which statement is not always true? 1) ∠J ≅ ∠M 2) ∠G ≅ ∠T 3) ∠R ≅ ∠T 4) ∠G ≅ ∠S 3 As shown in the diagram below, AB and CD intersect at E, and AC BD . 2 Given right triangle ABC with a right angle at C, m∠B = 61° . Given right triangle RST with a right angle at T, m∠R = 29° . Which proportion in relation to is not correct? AB RT = 1) RS AC BC AB = 2) ST RS BC AC = 3) ST RT AB RS = 4) AC RT ABC and Given AEC ∼ CE EB = 1) DE EA AE AC = 2) BE BD EC BE = 3) AE ED ED AC = 4) EC BD RST 1 BED, which equation is true? Regents Exam Questions G.SRT.B.5: Similarity 1 Name: ________________________ www.jmap.org 6 Triangles ABC and DEF are drawn below. 4 In the diagram below, XS and YR intersect at Z. Segments XY and RS are drawn perpendicular to YR to form triangles XYZ and SRZ. If AB = 9, BC = 15, DE = 6, EF = 10 , and ∠B ≅ ∠E , which statement is true? 1) ∠CAB ≅ ∠DEF AB FE = 2) CB DE ABC ∼ DEF 3) AB FE = 4) DE CB Which statement is always true? 1) (XY)(SR) = (XZ)(RZ) 2) XYZ ≅ SRZ 3) XS ≅ YR YZ XY = 4) SR RZ 5 In the diagram below of right triangle AED, BC DE . 7 In the diagram below, ABC ∼ DEF . If AB = 6 and AC = 8, which statement will justify similarity by SAS? 1) DE = 9 , DF = 12, and ∠A ≅ ∠D 2) DE = 8 , DF = 10, and ∠A ≅ ∠D 3) DE = 36 , DF = 64 , and ∠C ≅ ∠F 4) DE = 15 , DF = 20 , and ∠C ≅ ∠F Which statement is always true? AC DE = 1) AE BC AB BC = 2) AD DE AC BC = 3) CE DE DE DB = 4) AB BC 2 Regents Exam Questions G.SRT.B.5: Similarity 1 Name: ________________________ www.jmap.org 8 In the diagram below, AC = 7.2 and CE = 2.4. 10 In the diagram below, BC connects points B and C on the congruent sides of isosceles triangle ADE, such that ABC is isosceles with vertex angle A. Which statement is not sufficient to prove ABC ∼ EDC ? 1) AB ED 2) DE = 2.7 and AB = 8.1 3) CD = 3.6 and BC = 10.8 4) DE = 3.0 , AB = 9.0, CD = 2.9, and BC = 8.7 If AB = 10, BD = 5, and DE = 12 , what is the length of BC ? 1) 6 2) 7 3) 8 4) 9 9 Using the information given below, which set of triangles can not be proven similar? 11 In the diagram below, AD intersects BE at C, and AB DE . 1) 2) If CD = 6.6 cm, DE = 3.4 cm, CE = 4.2 cm, and BC = 5.25 cm, what is the length of AC , to the nearest hundredth of a centimeter? 1) 2.70 2) 3.34 3) 5.28 4) 8.25 3) 4) 3 Regents Exam Questions G.SRT.B.5: Similarity 1 Name: ________________________ www.jmap.org 14 In ABC shown below, ∠ACB is a right angle, E is a point on AC , and ED is drawn perpendicular to hypotenuse AB. 12 In SCU shown below, points T and O are on SU and CU , respectively. Segment OT is drawn so that ∠C ≅ ∠OTU . If AB = 9, BC = 6, and DE = 4 , what is the length of AE ? 1) 5 2) 6 3) 7 4) 8 If TU = 4, OU = 5, and OC = 7, what is the length of ST ? 1) 5.6 2) 8.75 3) 11 4) 15 15 In the diagram below, AF , and DB intersect at C, and AD and FBE are drawn such that m∠D = 65° , m∠CBE = 115° , DC = 7.2, AC = 9.6, and FC = 21.6. 13 In triangle CHR, O is on HR , and D is on CR so that ∠H ≅ ∠RDO. If RD = 4, RO = 6 , and OH = 4, what is the length of CD? 2 1) 2 3 2 2) 6 3 3) 11 4) 15 What is the length of CB? 1) 3.2 2) 4.8 3) 16.2 4) 19.2 4 Regents Exam Questions G.SRT.B.5: Similarity 1 Name: ________________________ www.jmap.org 16 The ratio of similarity of BOY to GRL is 1:2. If BO = x + 3 and GR = 3x − 1, then the length of GR is 1) 5 2) 7 3) 10 4) 20 20 The aspect ratio (the ratio of screen width to height) of a rectangular flat-screen television is 16:9. The length of the diagonal of the screen is the television's screen size. Determine and state, to the nearest inch, the screen size (diagonal) of this flat-screen television with a screen height of 20.6 inches. 17 Triangles RST and XYZ are drawn below. If RS = 6 , ST = 14, XY = 9, YZ = 21, and ∠S ≅ ∠Y , is RST similar to XYZ ? Justify your answer. 21 In the model below, a support wire for a telephone pole is attached to the pole and anchored to a stake in the ground 15 feet from the base of the telephone pole. Jamal places a 6-foot wooden pole under the support wire parallel to the telephone pole, such that one end of the pole is on the ground and the top of the pole is touching the support wire. He measures the distance between the bottom of the pole and the stake in the ground. 18 To find the distance across a pond from point B to point C, a surveyor drew the diagram below. The measurements he made are indicated on his diagram. Use the surveyor's information to determine and state the distance from point B to point C, to the nearest yard. Jamal says he can approximate how high the support wire attaches to the telephone pole by using similar triangles. Explain why the triangles are similar. 19 A flagpole casts a shadow 16.60 meters long. Tim stands at a distance of 12.45 meters from the base of the flagpole, such that the end of Tim's shadow meets the end of the flagpole's shadow. If Tim is 1.65 meters tall, determine and state the height of the flagpole to the nearest tenth of a meter. 5 ID: A G.SRT.B.5: Similarity 1 Answer Section 1 ANS: 2 2 ANS: 1 ABC ∼ REF: 012003geo RST REF: 011908geo 3 ANS: 2 4 ANS: 4 5 ANS: 2 ACB ∼ AED REF: 6 ANS: AB = BC REF: 081519geo REF: 011817geo 061811geo 3 DE EF 9 6 = 15 10 90 = 90 REF: 061515geo 7 ANS: 1 6 9 = 8 12 REF: 011613geo 8 ANS: 2 (1) AA; (3) SAS; (4) SSS. answer to this question. NYSED has stated that all students should be awarded credit regardless of their REF: 061724geo 9 ANS: 3 12 4 32 8 = 2) AA 3) ≠ 4) SAS 1) 3 9 16 2 REF: 061605geo 10 ANS: 3 10 15 = 12 x x=8 REF: 081918geo 1 ID: A 11 ANS: 4 6.6 4.2 = 5.25 x 4.2x = 34.65 x = 8.25 REF: 081705geo 12 ANS: 3 12 x = 15 − 4 = 11 5 4 x = 15 REF: 011624geo 13 ANS: 3 x 6 CD = 15 − 4 = 11 = 10 4 x = 15 REF: 081612geo 14 ANS: 2 4 6 = x 9 x=6 REF: 061915geo 15 ANS: 3 CFB ∼ CAD CB CD = CF CA x 7.2 = 21.6 9.6 x = 16.2 REF: 061804geo 16 ANS: 4 1 x+3 = GR = 3(7) − 1 = 20 2 3x − 1 3x − 1 = 2x + 6 x=7 REF: 011620geo 2 ID: A 17 ANS: 6 9 = SAS 14 21 126 = 126 REF: 081529geo 18 ANS: 120 x = 230 315 x = 164 REF: 081527geo 19 ANS: 1.65 x = 4.15 16.6 4.15x = 27.39 x = 6.6 REF: 061531geo 20 ANS: x 16 D = 36.6 2 + 20.6 2 ≈ 42 = 20.6 9 x ≈ 36.6 REF: 011632geo 21 ANS: ABC ∼ AED by AA. ∠DAE ≅ ∠CAB because they are the same ∠. ∠DEA ≅ ∠CBA because they are both right ∠s. REF: 081829geo 3