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3.7 Answers - #1, 3-4, 6, 10, 11, 12, 16, 19 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 19. 1. 2. 3. 4. 5. 6. 7. Statement HJ ≅ MK ∠HJK ≅ ∠MKJ JK ≅ JK HJK ≅MKJ ∠HKJ ≅ ∠MJK JO ≅ KO JOK is an isosceles triangle Reason 1. 2. 3. 4. 5. 6. 7. Given Given Reflexive Property SAS (1,2,3) CPCTC If base angles are congruent, then opposite sides are congruent. Def of Isosceles 3.8 Answers - #1, 3, 6, 8, 15, 16 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. 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 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 16. This is a mega challenge problem!!! I want to see what you come up with and show work underneath the document camera!