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3.7 Answers - #1, 3-4, 6, 10, 11, 12, 16 1. 1. 2. 3. 4. 5. Statement AB ≅ AC ∠ABC ≅ ∠ACB ∠1 supp to ∠ABC ∠2 supp to ∠ACB ∠1 ≅ ∠2 Reason 1. Given 2. If two sides of a triangle are congruent, then the angles opp them are congruent 3. If 2 angles form a strt angle, then they are supp 4. If 2 angles form a strt angle, then they are supp 5. If two angles are supp to congruent angles, then they are congruent 3. Statement 1. SX ≅ TY 2. WX ≅ YZ 3. WX ≅ YZ 4. SWX ≅TZY 5. ∠RWX ≅ ∠RZY 6. RW ≅ RZ Reason 1. Given 2. Given 3. Given 4. SSS [1, 2, 3] 5. CPCTC 6. If two angles of a triangle are congruent, then the sides opp them are congruent 4. 1. 2. 3. 4. Statement ∠3 ≅ ∠6 ∠3 comp to ∠4 ∠6 comp to ∠5 ∠4 ≅ ∠5 5. EB ≅ EC 6. EBC is isos Reason 1. Given 2. Given 3. Given 4. If two angles are comp to congruent angles, then they are congruent 5. If two angles of a triangle are congruent, then the sides opp them are congruent 6. If at least two sides of a triangle are congruent, then the triangle is isos 6. Statement 1. ∠5 ≅ ∠6 2. JG is alt to FH 3. ∠JGF & ∠JGH are rt angles 4. ∠JGF ≅ ∠JGH 5. JG ≅ JG 6. FJG ≅HJG 7. FJ ≅ HJ 8. FJH is isos Reason 1. Given 2. Given 3. If a seg is an altitude of a triangle, then it forms rt angles with one of the sides 4. If two angles are rt angles, then they are congruent 5. Reflexive Property 6. ASA [ 1, 4, 5] 7. CPCTC 8. If at least two sides of a triangle are congruent, then the triangle is isos 10. Statement 1. O 2. XO ≅ WO 3. OX ≅ XW 4. WO ≅ XW 5. XOW is equilateral Reason 1. 2. 3. 4. 5. Given Radii of a circle are congruent Given Transitive Property If all three sides of a triangle are congruent, then the triangle is equilateral ∠ACB = 90° AC = 2x − 20 BC = x + 20 3x = 90 AC = 2(30) − 20 = 60 − 20 = 40 BC = 30 + 20 = 50 x = 30 No, ABC is not isos, because no sides are congruent 11. a. Since QS & QP are both radii of Q , QS ≅ QP . If the sides of a triangle are congruent, then the angles opposite them are congruent. So m∠P = 36° = m∠PSQ . b. ∠PSR is a rt angle, so m∠R = 180 − 90 − 36 = 54° 12. 16. Statement 1. PR ≅ ST 2. RS ≅ RS 3. PS ≅ RT 4. 5. 6. 7. NP ≅ VT ∠P ≅ ∠T NPS ≅VTR ∠S ≅ ∠R 8. RW ≅ SW 9. WRS is isos Reason 1. Given 2. Reflexive Property 3. Addition Property 4. Given 5. Given 6. SAS [3, 4, 5] 7. CPCTC 8. If two angles of a triangle are congruent, then the sides opp them are congruent 9. If at least two sides of a triangle are congruent, then the triangle is isos 3.8 Answers - #1, 3, 6, 8, 15 1. Statement 1. GJ is alt to HK 2. GJ ⊥ HK 3. ∠GJK is a rt angle 4. ∠GJH is a rt angle 5. HG ≅ KG 6. GJ ≅ GJ 7. HGJ ≅KGJ 3. Statement 1. O 2. OY ≅ OZ 3. YO ⊥ YX 4. ∠OYX is a rt angle 5. ZO ⊥ ZX 6. ∠OZX is a rt angle 7. Draw OX 8. OX ≅ OX 9. YOX ≅ZOX 10. YX ≅ ZX Reason 1. Given 2. If a seg is an alt, then it is perpendicular to the opp side 3. If 2 segs are perpendicular, then they forms right angles 4. If 2 segs are perpendicular, then they forms right angles 5. Given 6. Reflexive Property 7. HL [3, 4, 5, 6] Reason 1. Given 2. All radii of a circle are congruent 3. Given 4. If 2 segs are perpendicular, then they forms right angles 5. Given 6. If 2 segs are perpendicular, then they forms right angles 7. 2 points determine a line, ray or a segment 8. Reflexive Property 9. HL [2, 4, 6, 8] 10. CPCTC 6. Statement 1. GH ≅ GK 2. GJ is alt to HK 3. GJ ⊥ HK 4. ∠GJK is a rt angle 5. ∠GJH is a rt angle 6. 7. 8. 9. GJ ≅ GJ HGJ ≅KGJ ∠HGJ ≅ ∠KGJ GJ bis ∠HGK Reason 1. Given 2. Given 3. If a seg is an alt, then it is perpendicular to the opp side 4. If 2 segs are perpendicular, then they forms right angles 5. If 2 segs are perpendicular, then they forms right angles 6. Reflexive Property 7. HL [1, 4, 5, 6] 8. CPCTC 9. If a ray divides an angle into two congruent angles, then it bisects the angle 8. Statement 1. BD ⊥ CF 2. ∠GJK is a rt angle 3. GE ⊥ CF 4. ∠GEF is a rt angle 5. CE ≅ DF 6. CD ≅ EF 7. BC ≅ GF 8. BCD ≅GFE 9. ∠C ≅ ∠F 10. AC ≅ AF 11. ACF is isos triangle 15. a. (4, 0) b. CPCTC c. ( 4 − (−2) = 6 XR = 4 + 6 = 10 R = (10,0) d. QS = 9 PR = 10 − (−2) = 12 1 A = (9)(12) = 54 2 Reason 1. Given 2. If 2 segs are perpendicular, then they forms right angles 3. Given 4. If 2 segs are perpendicular, then they forms right angles 5. Given 6. Subtraction Property 7. Given 8. HL [2, 4, 6, 7] 9. CPCTC 10. If two angles of a triangle are congruent, then the sides opposite them are congruent 11. If at least two sides of a triangle are congruent, then the triangle is isos