Download 3.7 Answers - #1, 3-4, 6, 10, 11, 12, 16, 19 1

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! 