Download 3.7 Answers - #1, 3-4, 6, 10, 11, 12, 16 1. Statement

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