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Lesson 4.7 • Flowchart Thinking Name Period Date Complete or write a flowchart for each proof. SR and PQ SR 1. Given: PQ S R QR Show: SP P Flowchart Proof Q Given PQ SR __________________ __________________ PQS ______ SP QR _________________ __________________ QS ______ __________________ KI 2. Given: Kite KITE with KE I bisects EKI and ETI Show: KT K Flowchart Proof T E KE KI ETK ITK ______________ _______________ __________________ KET ______ KITE is a kite ______________ ________________ Definition of bisect __________________ ______________ 3. Given: ABCD is a parallelogram Show: A C D A C B Flowchart Proof AB CD ABCD is a parallelogram _____________ Definition of ___________ _________________________ Same segment ____________ _____________ ______________ _____________ Discovering Geometry Practice Your Skills ©2003 Key Curriculum Press CHAPTER 4 29 9. ABE DEB (ASA or SAA); DEB BCD (ASA or SAA); ABE BCD (Both are congruent to DEB.) 8 and 10. Q(18, 9), R(20, 7). Slope BC slope QR 8. They have the same slope so they are parallel. CF (see Exercise 10). 11. Possible answer: DE DEF CFE because both are right angles, FE because they are the same segments. So, EF FD by CPCTC. DEF CFE by SAS. EC 12. Possible answer: Because TP RA and RT , PTR ART are given and TR being the same segment, PTR ART RP by CPCTC. by SAS and TA LESSON 4.6 • Corresponding Parts of Congruent Triangles LESSON 4.7 • Flowchart Thinking 1. SSS, SAS, ASA, SAA 1. (See flowchart proof at bottom of page.) 2. Third Angle Conjecture (or CPCTC after SAA) 2. (See flowchart proof at bottom of page.) and QR are 3. Triangles are congruent by SAA. BC corresponding parts of congruent triangles. 4. AIA Conjecture 5. AIA Conjecture 6. ASA 7. CPCTC 3. (See flowchart proof at bottom of page.) LESSON 4.8 • Proving Isosceles Triangle Conjectures 1. AD 8 2. mACD 36° 1 3. mB 71°, CB 192 4. mE 60° 5. AN 17 6. Perimeter ABCD 104 ZX by CPCTC. 8. YWM ZXM by SAS. YW BD by CPCTC. 9. ACD BCD by SAS. AD 10. Possible answer: DE and CF are both the distance and AB . Because the lines are parallel, between DC CF . the distances are equal. So, DE Lesson 4.7, Exercises 1, 2, 3 1. PQ SR Given PQ SR PQS RSQ PQS RSQ SP QR Given AIA Conjecture SAS Conjecture CPCTC QS QS Same segment 2. KE KI Given ETK ITK KITE is a kite TE TI KET KIT CPCTC KT bisects EKI and ETI Given Definition of kite SSS Conjecture EKT IKT Definition of bisect CPCTC KT KT Same segment 3. ABD CDB AB CD ABCD is a parallelogram Definition of parallelogram Given AIA Conjecture BD DB BDA DBC A C Same segment ASA Conjecture CPCTC AD CB Definition of parallelogram Discovering Geometry Practice Your Skills ©2003 Key Curriculum Press ADB CBD AIA Conjecture ANSWERS 97 7. (See flowchart proof at bottom of page.) 6. 170°; 36 sides 7. 15 sides 8. Given: Isosceles ABC BC and with AC median CD bisects ACB Show: CD 8. x 105° 9. x 105° Flowchart Proof C 10. x 18° 11. mHFD 147° LESSON 5.2 • Exterior Angles of a Polygon A D B CD is a median Given AC BC AD BD CD CD Given Definition of median Same segment ADC BDC 2 1. a 64°, b 1383° 2. a 102°, b 9° 3. a 156°, b 132°, c 108° 4. 12 sides 5. 24 sides 6. 4 sides 7. 6 sides 8. mTXS 30°, mSXP 18°, mPXH 12°, mHXO 15°, mOXY 45° 9. Each exterior angle is cut in half. SSS Conjecture 10. a 135°, b 40°, c 105°, d 135° ACD BCD 11. CPCTC CD bisects ACB Definition of bisect 12. LESSON 5.1 • Polygon Sum Conjecture 1. a 103°, b 103°, c 97°, d 83°, e 154° 108° 108° 108° 2. x 121.7°, y 130° 3. p 172°, q 116°, r 137°, s 90°, t 135° 4. a 92°, b 44°, c 51°, d 85°, e 44°, f 136° 5. mE 150° 3. x 64°, y 43° 70° D A LESSON 5.3 • Kite and Trapezoid Properties 2. x 124°, y 56° 110° 125° 85° 108° 1. x 30 C B 108° 4. x 12°, y 49° 150° E Lesson 4.8, Exercise 7 CD CD Same segment CD is an altitude Given 98 ADC and BDC are right angles Definition of altitude ANSWERS ADC BDC ADC BDC AD BD CD is a median Both are right angles SAA Conjecture CPCTC Definition of median AC BC A B Given Converse of IT Discovering Geometry Practice Your Skills ©2003 Key Curriculum Press